---
_id: '2120'
abstract:
- lang: eng
  text: 'We consider the linear stochastic Cauchy problem dX (t) =AX (t) dt +B dWH
    (t), t≥ 0, where A generates a C0-semigroup on a Banach space E, WH is a cylindrical
    Brownian motion over a Hilbert space H, and B: H → E is a bounded operator. Assuming
    the existence of a unique minimal invariant measure μ∞, let Lp denote the realization
    of the Ornstein-Uhlenbeck operator associated with this problem in Lp (E, μ∞).
    Under suitable assumptions concerning the invariance of the range of B under the
    semigroup generated by A, we prove the following domain inclusions, valid for
    1 < p ≤ 2: Image omitted. Here WHk, p (E, μinfin; denotes the kth order Sobolev
    space of functions with Fréchet derivatives up to order k in the direction of
    H. No symmetry assumptions are made on L p.'
acknowledgement: The authors are supported by the ‘VIDI subsidie’ 639.032.201 of the
  Netherlands Organization for Scientific Research (NWO) and by the Research Training
  Network HPRN-CT-2002-00281.
author:
- first_name: Jan
  full_name: Jan Maas
  id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
  last_name: Maas
  orcid: 0000-0002-0845-1338
- first_name: Jan
  full_name: van Neerven, Jan M
  last_name: Van Neerven
citation:
  ama: Maas J, Van Neerven J. On the domain of non-symmetric Ornstein-Uhlenbeck operators
    in banach spaces. <i>Infinite Dimensional Analysis, Quantum Probability and Related
    Topics</i>. 2008;11(4):603-626. doi:<a href="https://doi.org/10.1142/S0219025708003245">10.1142/S0219025708003245</a>
  apa: Maas, J., &#38; Van Neerven, J. (2008). On the domain of non-symmetric Ornstein-Uhlenbeck
    operators in banach spaces. <i>Infinite Dimensional Analysis, Quantum Probability
    and Related Topics</i>. World Scientific Publishing. <a href="https://doi.org/10.1142/S0219025708003245">https://doi.org/10.1142/S0219025708003245</a>
  chicago: Maas, Jan, and Jan Van Neerven. “On the Domain of Non-Symmetric Ornstein-Uhlenbeck
    Operators in Banach Spaces.” <i>Infinite Dimensional Analysis, Quantum Probability
    and Related Topics</i>. World Scientific Publishing, 2008. <a href="https://doi.org/10.1142/S0219025708003245">https://doi.org/10.1142/S0219025708003245</a>.
  ieee: J. Maas and J. Van Neerven, “On the domain of non-symmetric Ornstein-Uhlenbeck
    operators in banach spaces,” <i>Infinite Dimensional Analysis, Quantum Probability
    and Related Topics</i>, vol. 11, no. 4. World Scientific Publishing, pp. 603–626,
    2008.
  ista: Maas J, Van Neerven J. 2008. On the domain of non-symmetric Ornstein-Uhlenbeck
    operators in banach spaces. Infinite Dimensional Analysis, Quantum Probability
    and Related Topics. 11(4), 603–626.
  mla: Maas, Jan, and Jan Van Neerven. “On the Domain of Non-Symmetric Ornstein-Uhlenbeck
    Operators in Banach Spaces.” <i>Infinite Dimensional Analysis, Quantum Probability
    and Related Topics</i>, vol. 11, no. 4, World Scientific Publishing, 2008, pp.
    603–26, doi:<a href="https://doi.org/10.1142/S0219025708003245">10.1142/S0219025708003245</a>.
  short: J. Maas, J. Van Neerven, Infinite Dimensional Analysis, Quantum Probability
    and Related Topics 11 (2008) 603–626.
date_created: 2018-12-11T11:55:50Z
date_published: 2008-12-04T00:00:00Z
date_updated: 2021-01-12T06:55:26Z
day: '04'
doi: 10.1142/S0219025708003245
extern: 1
intvolume: '        11'
issue: '4'
main_file_link:
- open_access: '1'
  url: http://repository.tudelft.nl/view/ir/uuid:c8eca915-d38b-4827-a4d9-e89baabb43a6/
month: '12'
oa: 1
page: 603 - 626
publication: Infinite Dimensional Analysis, Quantum Probability and Related Topics
publication_status: published
publisher: World Scientific Publishing
publist_id: '4914'
quality_controlled: 0
status: public
title: On the domain of non-symmetric Ornstein-Uhlenbeck operators in banach spaces
type: journal_article
volume: 11
year: '2008'
...
---
_id: '2121'
abstract:
- lang: eng
  text: Let H be a separable real Hubert space and let double struck F sign = (ℱt)t∈[0,T]
    be the augmented filtration generated by an H-cylindrical Brownian motion (WH(t))t∈[0,T]
    on a probability space (Ω, ℱ ℙ). We prove that if E is a UMD Banach space, 1 ≤
    p &lt; ∞, and F ∈ double struck D sign1,p(Ω E) is ℱT-measurable, then F = double
    struck E sign(F) + ∫0T Pdouble struck F sign(DF) dW H, where D is the Malliavin
    derivative of F and P double struck F sign is the projection onto the F-adapted
    elements in a suitable Banach space of Lp-stochastically integrable ℒ(H, E)-valued
    processes.
acknowledgement: 'Research supported by ARC Discovery Grant dp0558539. 2research supported
  by VIDI subsidy 639.032.201 and VICI subsidy 639.033.604 of the Netherlands organisation
  for scientific research (nwo). '
author:
- first_name: Jan
  full_name: van Neerven, Jan M
  last_name: Van Neerven
- first_name: Jan
  full_name: Jan Maas
  id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
  last_name: Maas
  orcid: 0000-0002-0845-1338
citation:
  ama: Van Neerven J, Maas J. A Clark-Ocone formula in UMD Banach spaces. <i>Electronic
    Communications in Probability</i>. 2008;13:151-164.
  apa: Van Neerven, J., &#38; Maas, J. (2008). A Clark-Ocone formula in UMD Banach
    spaces. <i>Electronic Communications in Probability</i>. Institute of Mathematical
    Statistics.
  chicago: Van Neerven, Jan, and Jan Maas. “A Clark-Ocone Formula in UMD Banach Spaces.”
    <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics,
    2008.
  ieee: J. Van Neerven and J. Maas, “A Clark-Ocone formula in UMD Banach spaces,”
    <i>Electronic Communications in Probability</i>, vol. 13. Institute of Mathematical
    Statistics, pp. 151–164, 2008.
  ista: Van Neerven J, Maas J. 2008. A Clark-Ocone formula in UMD Banach spaces. Electronic
    Communications in Probability. 13, 151–164.
  mla: Van Neerven, Jan, and Jan Maas. “A Clark-Ocone Formula in UMD Banach Spaces.”
    <i>Electronic Communications in Probability</i>, vol. 13, Institute of Mathematical
    Statistics, 2008, pp. 151–64.
  short: J. Van Neerven, J. Maas, Electronic Communications in Probability 13 (2008)
    151–164.
date_created: 2018-12-11T11:55:50Z
date_published: 2008-04-07T00:00:00Z
date_updated: 2021-01-12T06:55:26Z
day: '07'
extern: 1
intvolume: '        13'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/0709.2021
month: '04'
oa: 1
page: 151 - 164
publication: Electronic Communications in Probability
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '4915'
quality_controlled: 0
status: public
title: A Clark-Ocone formula in UMD Banach spaces
type: journal_article
volume: 13
year: '2008'
...
---
_id: '2146'
abstract:
- lang: eng
  text: 'We present an analytic model of thermal state-to-state rotationally inelastic
    collisions of polar molecules in electric fields. The model is based on the Fraunhofer
    scattering of matter waves and requires Legendre moments characterizing the “shape”
    of the target in the body-fixed frame as its input. The electric field orients
    the target in the space-fixed frame and thereby effects a striking alteration
    of the dynamical observables: both the phase and amplitude of the oscillations
    in the partial differential cross sections undergo characteristic field-dependent
    changes that transgress into the partial integral cross sections. As the cross
    sections can be evaluated for a field applied parallel or perpendicular to the
    relative velocity, the model also offers predictions about steric asymmetry. We
    exemplify the field-dependent quantum collision dynamics with the behavior of
    the Ne–OCS(Σ1) and Ar–NO(Π2) systems. A comparison with the close-coupling calculations
    available for the latter system [Chem. Phys. Lett.313, 491 (1999)] demonstrates
    the model’s ability to qualitatively explain the field dependence of all the scattering
    features observed.'
author:
- first_name: Mikhail
  full_name: Mikhail Lemeshko
  id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
  last_name: Lemeshko
  orcid: 0000-0002-6990-7802
- first_name: Břetislav
  full_name: Friedrich, Břetislav
  last_name: Friedrich
citation:
  ama: Lemeshko M, Friedrich B. An analytic model of rotationally inelastic collisions
    of polar molecules in electric fields. <i>Journal of Chemical Physics</i>. 2008;129(2).
    doi:<a href="https://doi.org/10.1063/1.2948392">10.1063/1.2948392</a>
  apa: Lemeshko, M., &#38; Friedrich, B. (2008). An analytic model of rotationally
    inelastic collisions of polar molecules in electric fields. <i>Journal of Chemical
    Physics</i>. American Institute of Physics. <a href="https://doi.org/10.1063/1.2948392">https://doi.org/10.1063/1.2948392</a>
  chicago: Lemeshko, Mikhail, and Břetislav Friedrich. “An Analytic Model of Rotationally
    Inelastic Collisions of Polar Molecules in Electric Fields.” <i>Journal of Chemical
    Physics</i>. American Institute of Physics, 2008. <a href="https://doi.org/10.1063/1.2948392">https://doi.org/10.1063/1.2948392</a>.
  ieee: M. Lemeshko and B. Friedrich, “An analytic model of rotationally inelastic
    collisions of polar molecules in electric fields,” <i>Journal of Chemical Physics</i>,
    vol. 129, no. 2. American Institute of Physics, 2008.
  ista: Lemeshko M, Friedrich B. 2008. An analytic model of rotationally inelastic
    collisions of polar molecules in electric fields. Journal of Chemical Physics.
    129(2).
  mla: Lemeshko, Mikhail, and Břetislav Friedrich. “An Analytic Model of Rotationally
    Inelastic Collisions of Polar Molecules in Electric Fields.” <i>Journal of Chemical
    Physics</i>, vol. 129, no. 2, American Institute of Physics, 2008, doi:<a href="https://doi.org/10.1063/1.2948392">10.1063/1.2948392</a>.
  short: M. Lemeshko, B. Friedrich, Journal of Chemical Physics 129 (2008).
date_created: 2018-12-11T11:55:58Z
date_published: 2008-07-01T00:00:00Z
date_updated: 2021-01-12T06:55:35Z
day: '01'
doi: 10.1063/1.2948392
extern: 1
intvolume: '       129'
issue: '2'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/0804.3318
month: '07'
oa: 1
publication: Journal of Chemical Physics
publication_status: published
publisher: American Institute of Physics
publist_id: '4878'
quality_controlled: 0
status: public
title: An analytic model of rotationally inelastic collisions of polar molecules in
  electric fields
type: journal_article
volume: 129
year: '2008'
...
---
_id: '2147'
abstract:
- lang: eng
  text: 'We present the physics of the quantum Zeno effect, whose gist is often expressed
    by invoking the adage &quot;a watched pot never boils&quot;. We review aspects
    of the theoretical and experimental work done on the effect since its inception
    in 1977, and mention some applications. We dedicate the article - with our very
    best wishes - to Rudolf Zahradnik at the occasion of his great jubilee. Perhaps
    Rudolf''s lasting youthfulness and freshness are due to that he himself had been
    frequently observed throughout his life: until the political turn-around in 1989
    by those who wished, by their surveillance, to prevent Rudolf from spoiling the
    youth by his personal culture and his passion for science and things beautiful
    and useful in general. This attempt had failed. Out of gratitude, the youth has
    infected Rudolf with its youthfulness. Chronically. Since 1989, Rudolf has been
    closely watched by the public at large. For the same traits of his as before,
    but with the opposite goal and for the benefit of all generations. We relish keeping
    him in sight...'
author:
- first_name: Mikhail
  full_name: Mikhail Lemeshko
  id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
  last_name: Lemeshko
  orcid: 0000-0002-6990-7802
- first_name: Břetislav
  full_name: Friedrich, Břetislav
  last_name: Friedrich
citation:
  ama: Lemeshko M, Friedrich B. Kvantový Zenonův jev aneb co nesejde z očí, nezestárne.
    <i>Chemicke Listy</i>. 2008;102(10):880-883.
  apa: Lemeshko, M., &#38; Friedrich, B. (2008). Kvantový Zenonův jev aneb co nesejde
    z očí, nezestárne. <i>Chemicke Listy</i>. Czech Society of Chemical Engineering.
  chicago: Lemeshko, Mikhail, and Břetislav Friedrich. “Kvantový Zenonův Jev Aneb
    Co Nesejde z Očí, Nezestárne.” <i>Chemicke Listy</i>. Czech Society of Chemical
    Engineering, 2008.
  ieee: M. Lemeshko and B. Friedrich, “Kvantový Zenonův jev aneb co nesejde z očí,
    nezestárne,” <i>Chemicke Listy</i>, vol. 102, no. 10. Czech Society of Chemical
    Engineering, pp. 880–883, 2008.
  ista: Lemeshko M, Friedrich B. 2008. Kvantový Zenonův jev aneb co nesejde z očí,
    nezestárne. Chemicke Listy. 102(10), 880–883.
  mla: Lemeshko, Mikhail, and Břetislav Friedrich. “Kvantový Zenonův Jev Aneb Co Nesejde
    z Očí, Nezestárne.” <i>Chemicke Listy</i>, vol. 102, no. 10, Czech Society of
    Chemical Engineering, 2008, pp. 880–83.
  short: M. Lemeshko, B. Friedrich, Chemicke Listy 102 (2008) 880–883.
date_created: 2018-12-11T11:55:59Z
date_published: 2008-10-01T00:00:00Z
date_updated: 2020-07-14T12:45:29Z
day: '01'
extern: 1
intvolume: '       102'
issue: '10'
month: '10'
page: 880 - 883
publication: Chemicke Listy
publication_status: published
publisher: Czech Society of Chemical Engineering
publist_id: '4877'
quality_controlled: 0
status: public
title: Kvantový Zenonův jev aneb co nesejde z očí, nezestárne
type: review
volume: 102
year: '2008'
...
---
_id: '2148'
abstract:
- lang: eng
  text: Despite the growing geological evidence that fluid boiling and vapour-liquid
    separation affect the distribution of metals in magmatic-hydrothermal systems
    significantly, there are few experimental data on the chemical status and partitioning
    of metals in the vapour and liquid phases. Here we report on an in situ measurement,
    using X-ray absorption fine structure (XAFS) spectroscopy, of antimony speciation
    and partitioning in the system Sb2O3-H2O-NaCl-HCl at 400°C and pressures 270–300
    bar corresponding to the vapour-liquid equilibrium. Experiments were performed
    using a spectroscopic cell which allows simultaneous determination of the total
    concentration and atomic environment of the absorbing element (Sb) in each phase.
    Results show that quantitative vapour-brine separation of a supercritical aqueous
    salt fluid can be achieved by a controlled decompression and monitoring the X-ray
    absorbance of the fluid phase. Antimony concentrations in equilibrium with Sb2O3
    (cubic, senarmontite) in the coexisting vapour and liquid phases and corresponding
    SbIII vapour-liquid partitioning coefficients are in agreement with recent data
    obtained using batch-reactor solubility techniques. The XAFS spectra analysis
    shows that hydroxy-chloride complexes, probably Sb(OH)2Cl0, are dominant both
    in the vapour and liquid phase in a salt-water system at acidic conditions. This
    first in situ XAFS study of element fractionation between coexisting volatile
    and dense phases opens new possibilities for systematic investigations of vapour-brine
    and fluid-melt immiscibility phenomena, avoiding many experimental artifacts common
    in less direct techniques.
author:
- first_name: Gleb
  full_name: Pokrovski, Gleb S
  last_name: Pokrovski
- first_name: Jacques
  full_name: Roux, Jacques L
  last_name: Roux
- first_name: Jean
  full_name: Hazemann, Jean L
  last_name: Hazemann
- first_name: Anastassia
  full_name: Borisova, Anastassia Y
  last_name: Borisova
- first_name: Anastasia
  full_name: Gonchar, Anastasia A
  last_name: Gonchar
- first_name: Mikhail
  full_name: Mikhail Lemeshko
  id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
  last_name: Lemeshko
  orcid: 0000-0002-6990-7802
citation:
  ama: Pokrovski G, Roux J, Hazemann J, Borisova A, Gonchar A, Lemeshko M. In situ
    X-ray absorption spectroscopy measurement of vapour-brine fractionation of antimony
    at hydrothermal conditions. <i>Mineralogical Magazine</i>. 2008;72(2):667-681.
    doi:<a href="https://doi.org/10.1180/minmag.2008.072.2.667 ">10.1180/minmag.2008.072.2.667
    </a>
  apa: Pokrovski, G., Roux, J., Hazemann, J., Borisova, A., Gonchar, A., &#38; Lemeshko,
    M. (2008). In situ X-ray absorption spectroscopy measurement of vapour-brine fractionation
    of antimony at hydrothermal conditions. <i>Mineralogical Magazine</i>. Mineralogical
    Society. <a href="https://doi.org/10.1180/minmag.2008.072.2.667 ">https://doi.org/10.1180/minmag.2008.072.2.667
    </a>
  chicago: Pokrovski, Gleb, Jacques Roux, Jean Hazemann, Anastassia Borisova, Anastasia
    Gonchar, and Mikhail Lemeshko. “In Situ X-Ray Absorption Spectroscopy Measurement
    of Vapour-Brine Fractionation of Antimony at Hydrothermal Conditions.” <i>Mineralogical
    Magazine</i>. Mineralogical Society, 2008. <a href="https://doi.org/10.1180/minmag.2008.072.2.667
    ">https://doi.org/10.1180/minmag.2008.072.2.667 </a>.
  ieee: G. Pokrovski, J. Roux, J. Hazemann, A. Borisova, A. Gonchar, and M. Lemeshko,
    “In situ X-ray absorption spectroscopy measurement of vapour-brine fractionation
    of antimony at hydrothermal conditions,” <i>Mineralogical Magazine</i>, vol. 72,
    no. 2. Mineralogical Society, pp. 667–681, 2008.
  ista: Pokrovski G, Roux J, Hazemann J, Borisova A, Gonchar A, Lemeshko M. 2008.
    In situ X-ray absorption spectroscopy measurement of vapour-brine fractionation
    of antimony at hydrothermal conditions. Mineralogical Magazine. 72(2), 667–681.
  mla: Pokrovski, Gleb, et al. “In Situ X-Ray Absorption Spectroscopy Measurement
    of Vapour-Brine Fractionation of Antimony at Hydrothermal Conditions.” <i>Mineralogical
    Magazine</i>, vol. 72, no. 2, Mineralogical Society, 2008, pp. 667–81, doi:<a
    href="https://doi.org/10.1180/minmag.2008.072.2.667 ">10.1180/minmag.2008.072.2.667
    </a>.
  short: G. Pokrovski, J. Roux, J. Hazemann, A. Borisova, A. Gonchar, M. Lemeshko,
    Mineralogical Magazine 72 (2008) 667–681.
date_created: 2018-12-11T11:55:59Z
date_published: 2008-04-01T00:00:00Z
date_updated: 2021-01-12T06:55:36Z
day: '01'
doi: '10.1180/minmag.2008.072.2.667 '
extern: 1
intvolume: '        72'
issue: '2'
month: '04'
page: 667 - 681
publication: Mineralogical Magazine
publication_status: published
publisher: Mineralogical Society
publist_id: '4876'
quality_controlled: 0
status: public
title: In situ X-ray absorption spectroscopy measurement of vapour-brine fractionation
  of antimony at hydrothermal conditions
type: journal_article
volume: 72
year: '2008'
...
---
_id: '224'
abstract:
- lang: eng
  text: Let n ≥ 4 and let Q ∈ [X1, ..., Xn] be a non-singular quadratic form. When
    Q is indefinite we provide new upper bounds for the least non-trivial integral
    solution to the equation Q = 0, and when Q is positive definite we provide improved
    upper bounds for the greatest positive integer k for which the equation Q = k
    is insoluble in integers, despite being soluble modulo every prime power.
author:
- first_name: Timothy D
  full_name: Timothy Browning
  id: 35827D50-F248-11E8-B48F-1D18A9856A87
  last_name: Browning
  orcid: 0000-0002-8314-0177
- first_name: Rainer
  full_name: Dietmann, Rainer
  last_name: Dietmann
citation:
  ama: Browning TD, Dietmann R. On the representation of integers by quadratic forms.
    <i>Proceedings of the London Mathematical Society</i>. 2008;96(2):389-416. doi:<a
    href="https://doi.org/10.1112/plms/pdm032">10.1112/plms/pdm032</a>
  apa: Browning, T. D., &#38; Dietmann, R. (2008). On the representation of integers
    by quadratic forms. <i>Proceedings of the London Mathematical Society</i>. John
    Wiley and Sons Ltd. <a href="https://doi.org/10.1112/plms/pdm032">https://doi.org/10.1112/plms/pdm032</a>
  chicago: Browning, Timothy D, and Rainer Dietmann. “On the Representation of Integers
    by Quadratic Forms.” <i>Proceedings of the London Mathematical Society</i>. John
    Wiley and Sons Ltd, 2008. <a href="https://doi.org/10.1112/plms/pdm032">https://doi.org/10.1112/plms/pdm032</a>.
  ieee: T. D. Browning and R. Dietmann, “On the representation of integers by quadratic
    forms,” <i>Proceedings of the London Mathematical Society</i>, vol. 96, no. 2.
    John Wiley and Sons Ltd, pp. 389–416, 2008.
  ista: Browning TD, Dietmann R. 2008. On the representation of integers by quadratic
    forms. Proceedings of the London Mathematical Society. 96(2), 389–416.
  mla: Browning, Timothy D., and Rainer Dietmann. “On the Representation of Integers
    by Quadratic Forms.” <i>Proceedings of the London Mathematical Society</i>, vol.
    96, no. 2, John Wiley and Sons Ltd, 2008, pp. 389–416, doi:<a href="https://doi.org/10.1112/plms/pdm032">10.1112/plms/pdm032</a>.
  short: T.D. Browning, R. Dietmann, Proceedings of the London Mathematical Society
    96 (2008) 389–416.
date_created: 2018-12-11T11:45:18Z
date_published: 2008-03-01T00:00:00Z
date_updated: 2021-01-12T06:56:13Z
day: '01'
doi: 10.1112/plms/pdm032
extern: 1
intvolume: '        96'
issue: '2'
month: '03'
page: 389 - 416
publication: Proceedings of the London Mathematical Society
publication_status: published
publisher: John Wiley and Sons Ltd
publist_id: '7688'
quality_controlled: 0
status: public
title: On the representation of integers by quadratic forms
type: journal_article
volume: 96
year: '2008'
...
---
_id: '225'
abstract:
- lang: eng
  text: We revisit recent work of Heath-Brown on the average order of the quantity
    r(L1(x))⋯r(L4(x)), for suitable binary linear forms L1,...,L4, as x=(x1,x2) ranges
    over quite general regions in ℤ2. In addition to improving the error term in Heath-Browns
    estimate, we generalise his result to cover a wider class of linear forms.
acknowledgement: "EP/E053262/1\tEngineering and Physical Sciences Research Council"
author:
- first_name: Régis
  full_name: de la Bretèche, Régis
  last_name: De La Bretèche
- first_name: Timothy D
  full_name: Timothy Browning
  id: 35827D50-F248-11E8-B48F-1D18A9856A87
  last_name: Browning
  orcid: 0000-0002-8314-0177
citation:
  ama: De La Bretèche R, Browning TD. Binary linear forms as sums of two squares.
    <i>Compositio Mathematica</i>. 2008;144(6):1375-1402. doi:<a href="https://doi.org/10.1112/S0010437X08003692">10.1112/S0010437X08003692</a>
  apa: De La Bretèche, R., &#38; Browning, T. D. (2008). Binary linear forms as sums
    of two squares. <i>Compositio Mathematica</i>. Cambridge University Press. <a
    href="https://doi.org/10.1112/S0010437X08003692">https://doi.org/10.1112/S0010437X08003692</a>
  chicago: De La Bretèche, Régis, and Timothy D Browning. “Binary Linear Forms as
    Sums of Two Squares.” <i>Compositio Mathematica</i>. Cambridge University Press,
    2008. <a href="https://doi.org/10.1112/S0010437X08003692">https://doi.org/10.1112/S0010437X08003692</a>.
  ieee: R. De La Bretèche and T. D. Browning, “Binary linear forms as sums of two
    squares,” <i>Compositio Mathematica</i>, vol. 144, no. 6. Cambridge University
    Press, pp. 1375–1402, 2008.
  ista: De La Bretèche R, Browning TD. 2008. Binary linear forms as sums of two squares.
    Compositio Mathematica. 144(6), 1375–1402.
  mla: De La Bretèche, Régis, and Timothy D. Browning. “Binary Linear Forms as Sums
    of Two Squares.” <i>Compositio Mathematica</i>, vol. 144, no. 6, Cambridge University
    Press, 2008, pp. 1375–402, doi:<a href="https://doi.org/10.1112/S0010437X08003692">10.1112/S0010437X08003692</a>.
  short: R. De La Bretèche, T.D. Browning, Compositio Mathematica 144 (2008) 1375–1402.
date_created: 2018-12-11T11:45:18Z
date_published: 2008-11-01T00:00:00Z
date_updated: 2021-01-12T06:56:17Z
day: '01'
doi: 10.1112/S0010437X08003692
extern: 1
intvolume: '       144'
issue: '6'
month: '11'
page: 1375 - 1402
publication: Compositio Mathematica
publication_status: published
publisher: Cambridge University Press
publist_id: '7687'
quality_controlled: 0
status: public
title: Binary linear forms as sums of two squares
type: journal_article
volume: 144
year: '2008'
...
---
_id: '2331'
abstract:
- lang: eng
  text: We present a review of recent work on the mathematical aspects of the BCS
    gap equation, covering our results of Ref. 9 as well our recent joint work with
    Hamza and Solovej and with Frank and Naboko, respectively. In addition, we mention
    some related new results.
author:
- first_name: Christian
  full_name: Hainzl, Christian
  last_name: Hainzl
- first_name: Robert
  full_name: Robert Seiringer
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: 'Hainzl C, Seiringer R.  Spectral properties of the BCS gap equation of superfluidity.
    In: World Scientific Publishing; 2008:117-136. doi:<a href="https://doi.org/10.1142/9789812832382_0009">10.1142/9789812832382_0009</a>'
  apa: 'Hainzl, C., &#38; Seiringer, R. (2008).  Spectral properties of the BCS gap
    equation of superfluidity (pp. 117–136). Presented at the QMath: Mathematical
    Results in Quantum Physics, World Scientific Publishing. <a href="https://doi.org/10.1142/9789812832382_0009">https://doi.org/10.1142/9789812832382_0009</a>'
  chicago: Hainzl, Christian, and Robert Seiringer. “ Spectral Properties of the BCS
    Gap Equation of Superfluidity,” 117–36. World Scientific Publishing, 2008. <a
    href="https://doi.org/10.1142/9789812832382_0009">https://doi.org/10.1142/9789812832382_0009</a>.
  ieee: 'C. Hainzl and R. Seiringer, “ Spectral properties of the BCS gap equation
    of superfluidity,” presented at the QMath: Mathematical Results in Quantum Physics,
    2008, pp. 117–136.'
  ista: 'Hainzl C, Seiringer R. 2008.  Spectral properties of the BCS gap equation
    of superfluidity. QMath: Mathematical Results in Quantum Physics, 117–136.'
  mla: Hainzl, Christian, and Robert Seiringer. <i> Spectral Properties of the BCS
    Gap Equation of Superfluidity</i>. World Scientific Publishing, 2008, pp. 117–36,
    doi:<a href="https://doi.org/10.1142/9789812832382_0009">10.1142/9789812832382_0009</a>.
  short: C. Hainzl, R. Seiringer, in:, World Scientific Publishing, 2008, pp. 117–136.
conference:
  name: 'QMath: Mathematical Results in Quantum Physics'
date_created: 2018-12-11T11:57:02Z
date_published: 2008-08-01T00:00:00Z
date_updated: 2021-01-12T06:56:50Z
day: '01'
doi: 10.1142/9789812832382_0009
extern: 1
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/0802.0446
month: '08'
oa: 1
page: 117 - 136
publication_status: published
publisher: World Scientific Publishing
publist_id: '4595'
quality_controlled: 0
status: public
title: ' Spectral properties of the BCS gap equation of superfluidity'
type: conference
year: '2008'
...
---
_id: '2332'
abstract:
- lang: eng
  text: We present a rigorous proof of the appearance of quantized vortices in dilute
    trapped Bose gases with repulsive two-body interactions subject to rotation, which
    was obtained recently in joint work with Elliott Lieb.14 Starting from the many-body
    Schrödinger equation, we show that the ground state of such gases is, in a suitable
    limit, well described by the nonlinear Gross-Pitaevskii equation. In the case
    of axially symmetric traps, our results show that the appearance of quantized
    vortices causes spontaneous symmetry breaking in the ground state.
author:
- first_name: Robert
  full_name: Robert Seiringer
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: 'Seiringer R. Vortices and Spontaneous Symmetry Breaking in Rotating Bose Gases.
    In: World Scientific Publishing; 2008:241-254. doi:<a href="https://doi.org/10.1142/9789812832382_0017">10.1142/9789812832382_0017</a>'
  apa: 'Seiringer, R. (2008). Vortices and Spontaneous Symmetry Breaking in Rotating
    Bose Gases (pp. 241–254). Presented at the QMath: Mathematical Results in Quantum
    Physics, World Scientific Publishing. <a href="https://doi.org/10.1142/9789812832382_0017">https://doi.org/10.1142/9789812832382_0017</a>'
  chicago: Seiringer, Robert. “Vortices and Spontaneous Symmetry Breaking in Rotating
    Bose Gases,” 241–54. World Scientific Publishing, 2008. <a href="https://doi.org/10.1142/9789812832382_0017">https://doi.org/10.1142/9789812832382_0017</a>.
  ieee: 'R. Seiringer, “Vortices and Spontaneous Symmetry Breaking in Rotating Bose
    Gases,” presented at the QMath: Mathematical Results in Quantum Physics, 2008,
    pp. 241–254.'
  ista: 'Seiringer R. 2008. Vortices and Spontaneous Symmetry Breaking in Rotating
    Bose Gases. QMath: Mathematical Results in Quantum Physics, 241–254.'
  mla: Seiringer, Robert. <i>Vortices and Spontaneous Symmetry Breaking in Rotating
    Bose Gases</i>. World Scientific Publishing, 2008, pp. 241–54, doi:<a href="https://doi.org/10.1142/9789812832382_0017">10.1142/9789812832382_0017</a>.
  short: R. Seiringer, in:, World Scientific Publishing, 2008, pp. 241–254.
conference:
  name: 'QMath: Mathematical Results in Quantum Physics'
date_created: 2018-12-11T11:57:02Z
date_published: 2008-12-30T00:00:00Z
date_updated: 2021-01-12T06:56:50Z
day: '30'
doi: 10.1142/9789812832382_0017
extern: 1
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/0801.0427
month: '12'
oa: 1
page: 241 - 254
publication_status: published
publisher: World Scientific Publishing
publist_id: '4594'
quality_controlled: 0
status: public
title: Vortices and Spontaneous Symmetry Breaking in Rotating Bose Gases
type: conference
year: '2008'
...
---
_id: '2374'
abstract:
- lang: eng
  text: A lower bound is derived on the free energy (per unit volume) of a homogeneous
    Bose gas at density Q and temperature T. In the dilute regime, i.e., when a3 1,
    where a denotes the scattering length of the pair-interaction potential, our bound
    differs to leading order from the expression for non-interacting particles by
    the term 4πa(2 2}-[ - c]2+). Here, c(T) denotes the critical density for Bose-Einstein
    condensation (for the non-interacting gas), and [ · ]+ = max{ ·, 0} denotes the
    positive part. Our bound is uniform in the temperature up to temperatures of the
    order of the critical temperature, i.e., T ~ 2/3 or smaller. One of the key ingredients
    in the proof is the use of coherent states to extend the method introduced in
    [17] for estimating correlations to temperatures below the critical one.
author:
- first_name: Robert
  full_name: Robert Seiringer
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: 'Seiringer R. Free energy of a dilute Bose gas: Lower bound. <i>Communications
    in Mathematical Physics</i>. 2008;279(3):595-636. doi:<a href="https://doi.org/10.1007/s00220-008-0428-2">10.1007/s00220-008-0428-2</a>'
  apa: 'Seiringer, R. (2008). Free energy of a dilute Bose gas: Lower bound. <i>Communications
    in Mathematical Physics</i>. Springer. <a href="https://doi.org/10.1007/s00220-008-0428-2">https://doi.org/10.1007/s00220-008-0428-2</a>'
  chicago: 'Seiringer, Robert. “Free Energy of a Dilute Bose Gas: Lower Bound.” <i>Communications
    in Mathematical Physics</i>. Springer, 2008. <a href="https://doi.org/10.1007/s00220-008-0428-2">https://doi.org/10.1007/s00220-008-0428-2</a>.'
  ieee: 'R. Seiringer, “Free energy of a dilute Bose gas: Lower bound,” <i>Communications
    in Mathematical Physics</i>, vol. 279, no. 3. Springer, pp. 595–636, 2008.'
  ista: 'Seiringer R. 2008. Free energy of a dilute Bose gas: Lower bound. Communications
    in Mathematical Physics. 279(3), 595–636.'
  mla: 'Seiringer, Robert. “Free Energy of a Dilute Bose Gas: Lower Bound.” <i>Communications
    in Mathematical Physics</i>, vol. 279, no. 3, Springer, 2008, pp. 595–636, doi:<a
    href="https://doi.org/10.1007/s00220-008-0428-2">10.1007/s00220-008-0428-2</a>.'
  short: R. Seiringer, Communications in Mathematical Physics 279 (2008) 595–636.
date_created: 2018-12-11T11:57:17Z
date_published: 2008-05-01T00:00:00Z
date_updated: 2021-01-12T06:57:06Z
day: '01'
doi: 10.1007/s00220-008-0428-2
extern: 1
intvolume: '       279'
issue: '3'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/math-ph/0608069
month: '05'
oa: 1
page: 595 - 636
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4551'
quality_controlled: 0
status: public
title: 'Free energy of a dilute Bose gas: Lower bound'
type: journal_article
volume: 279
year: '2008'
...
---
_id: '2376'
abstract:
- lang: eng
  text: We derive upper and lower bounds on the critical temperature Tc and the energy
    gap Ξ (at zero temperature) for the BCS gap equation, describing spin- 1 2 fermions
    interacting via a local two-body interaction potential λV(x). At weak coupling
    λ 1 and under appropriate assumptions on V(x), our bounds show that Tc ∼A exp(-B/λ)
    and Ξ∼C exp(-B/λ) for some explicit coefficients A, B, and C depending on the
    interaction V(x) and the chemical potential μ. The ratio A/C turns out to be a
    universal constant, independent of both V(x) and μ. Our analysis is valid for
    any μ; for small μ, or low density, our formulas reduce to well-known expressions
    involving the scattering length of V(x).
author:
- first_name: Christian
  full_name: Hainzl, Christian
  last_name: Hainzl
- first_name: Robert
  full_name: Robert Seiringer
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Hainzl C, Seiringer R. Critical temperature and energy gap for the BCS equation.
    <i>Physical Review B - Condensed Matter and Materials Physics</i>. 2008;77(18).
    doi:<a href="https://doi.org/10.1103/PhysRevB.77.184517">10.1103/PhysRevB.77.184517</a>
  apa: Hainzl, C., &#38; Seiringer, R. (2008). Critical temperature and energy gap
    for the BCS equation. <i>Physical Review B - Condensed Matter and Materials Physics</i>.
    American Physical Society. <a href="https://doi.org/10.1103/PhysRevB.77.184517">https://doi.org/10.1103/PhysRevB.77.184517</a>
  chicago: Hainzl, Christian, and Robert Seiringer. “Critical Temperature and Energy
    Gap for the BCS Equation.” <i>Physical Review B - Condensed Matter and Materials
    Physics</i>. American Physical Society, 2008. <a href="https://doi.org/10.1103/PhysRevB.77.184517">https://doi.org/10.1103/PhysRevB.77.184517</a>.
  ieee: C. Hainzl and R. Seiringer, “Critical temperature and energy gap for the BCS
    equation,” <i>Physical Review B - Condensed Matter and Materials Physics</i>,
    vol. 77, no. 18. American Physical Society, 2008.
  ista: Hainzl C, Seiringer R. 2008. Critical temperature and energy gap for the BCS
    equation. Physical Review B - Condensed Matter and Materials Physics. 77(18).
  mla: Hainzl, Christian, and Robert Seiringer. “Critical Temperature and Energy Gap
    for the BCS Equation.” <i>Physical Review B - Condensed Matter and Materials Physics</i>,
    vol. 77, no. 18, American Physical Society, 2008, doi:<a href="https://doi.org/10.1103/PhysRevB.77.184517">10.1103/PhysRevB.77.184517</a>.
  short: C. Hainzl, R. Seiringer, Physical Review B - Condensed Matter and Materials
    Physics 77 (2008).
date_created: 2018-12-11T11:57:18Z
date_published: 2008-05-28T00:00:00Z
date_updated: 2021-01-12T06:57:06Z
day: '28'
doi: 10.1103/PhysRevB.77.184517
extern: 1
intvolume: '        77'
issue: '18'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/0801.4159
month: '05'
oa: 1
publication: Physical Review B - Condensed Matter and Materials Physics
publication_status: published
publisher: American Physical Society
publist_id: '4550'
quality_controlled: 0
status: public
title: Critical temperature and energy gap for the BCS equation
type: journal_article
volume: 77
year: '2008'
...
---
_id: '2377'
abstract:
- lang: eng
  text: We prove that the critical temperature for the BCS gap equation is given by
    T c = μ ( 8\π e γ-2+ o(1)) e π/(2μa) in the low density limit μ→ 0, with γ denoting
    Euler's constant. The formula holds for a suitable class of interaction potentials
    with negative scattering length a in the absence of bound states.
author:
- first_name: Christian
  full_name: Hainzl, Christian
  last_name: Hainzl
- first_name: Robert
  full_name: Robert Seiringer
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Hainzl C, Seiringer R. The BCS critical temperature for potentials with negative
    scattering length. <i>Letters in Mathematical Physics</i>. 2008;84(2-3):99-107.
    doi:<a href="https://doi.org/10.1007/s11005-008-0242-y">10.1007/s11005-008-0242-y</a>
  apa: Hainzl, C., &#38; Seiringer, R. (2008). The BCS critical temperature for potentials
    with negative scattering length. <i>Letters in Mathematical Physics</i>. Springer.
    <a href="https://doi.org/10.1007/s11005-008-0242-y">https://doi.org/10.1007/s11005-008-0242-y</a>
  chicago: Hainzl, Christian, and Robert Seiringer. “The BCS Critical Temperature
    for Potentials with Negative Scattering Length.” <i>Letters in Mathematical Physics</i>.
    Springer, 2008. <a href="https://doi.org/10.1007/s11005-008-0242-y">https://doi.org/10.1007/s11005-008-0242-y</a>.
  ieee: C. Hainzl and R. Seiringer, “The BCS critical temperature for potentials with
    negative scattering length,” <i>Letters in Mathematical Physics</i>, vol. 84,
    no. 2–3. Springer, pp. 99–107, 2008.
  ista: Hainzl C, Seiringer R. 2008. The BCS critical temperature for potentials with
    negative scattering length. Letters in Mathematical Physics. 84(2–3), 99–107.
  mla: Hainzl, Christian, and Robert Seiringer. “The BCS Critical Temperature for
    Potentials with Negative Scattering Length.” <i>Letters in Mathematical Physics</i>,
    vol. 84, no. 2–3, Springer, 2008, pp. 99–107, doi:<a href="https://doi.org/10.1007/s11005-008-0242-y">10.1007/s11005-008-0242-y</a>.
  short: C. Hainzl, R. Seiringer, Letters in Mathematical Physics 84 (2008) 99–107.
date_created: 2018-12-11T11:57:19Z
date_published: 2008-06-01T00:00:00Z
date_updated: 2021-01-12T06:57:07Z
day: '01'
doi: 10.1007/s11005-008-0242-y
extern: 1
intvolume: '        84'
issue: 2-3
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/0803.3324
month: '06'
oa: 1
page: 99 - 107
publication: Letters in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4548'
quality_controlled: 0
status: public
title: The BCS critical temperature for potentials with negative scattering length
type: journal_article
volume: 84
year: '2008'
...
---
_id: '2378'
abstract:
- lang: eng
  text: We derive a lower bound on the ground state energy of the Hubbard model for
    given value of the total spin. In combination with the upper bound derived previously
    by Giuliani (J. Math. Phys. 48:023302, [2007]), our result proves that in the
    low density limit the leading order correction compared to the ground state energy
    of a non-interacting lattice Fermi gas is given by 8πaσ uσ d , where σ u(d) denotes
    the density of the spin-up (down) particles, and a is the scattering length of
    the contact interaction potential. This result extends previous work on the corresponding
    continuum model to the lattice case.
author:
- first_name: Robert
  full_name: Robert Seiringer
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
- first_name: Jun
  full_name: Yin, Jun
  last_name: Yin
citation:
  ama: Seiringer R, Yin J. Ground state energy of the low density hubbard model. <i>Journal
    of Statistical Physics</i>. 2008;131(6):1139-1154. doi:<a href="https://doi.org/10.1007/s10955-008-9527-x">10.1007/s10955-008-9527-x</a>
  apa: Seiringer, R., &#38; Yin, J. (2008). Ground state energy of the low density
    hubbard model. <i>Journal of Statistical Physics</i>. Springer. <a href="https://doi.org/10.1007/s10955-008-9527-x">https://doi.org/10.1007/s10955-008-9527-x</a>
  chicago: Seiringer, Robert, and Jun Yin. “Ground State Energy of the Low Density
    Hubbard Model.” <i>Journal of Statistical Physics</i>. Springer, 2008. <a href="https://doi.org/10.1007/s10955-008-9527-x">https://doi.org/10.1007/s10955-008-9527-x</a>.
  ieee: R. Seiringer and J. Yin, “Ground state energy of the low density hubbard model,”
    <i>Journal of Statistical Physics</i>, vol. 131, no. 6. Springer, pp. 1139–1154,
    2008.
  ista: Seiringer R, Yin J. 2008. Ground state energy of the low density hubbard model.
    Journal of Statistical Physics. 131(6), 1139–1154.
  mla: Seiringer, Robert, and Jun Yin. “Ground State Energy of the Low Density Hubbard
    Model.” <i>Journal of Statistical Physics</i>, vol. 131, no. 6, Springer, 2008,
    pp. 1139–54, doi:<a href="https://doi.org/10.1007/s10955-008-9527-x">10.1007/s10955-008-9527-x</a>.
  short: R. Seiringer, J. Yin, Journal of Statistical Physics 131 (2008) 1139–1154.
date_created: 2018-12-11T11:57:19Z
date_published: 2008-06-01T00:00:00Z
date_updated: 2021-01-12T06:57:07Z
day: '01'
doi: 10.1007/s10955-008-9527-x
extern: 1
intvolume: '       131'
issue: '6'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/0712.2810
month: '06'
oa: 1
page: 1139 - 1154
publication: Journal of Statistical Physics
publication_status: published
publisher: Springer
publist_id: '4549'
quality_controlled: 0
status: public
title: Ground state energy of the low density hubbard model
type: journal_article
volume: 131
year: '2008'
...
---
_id: '2379'
author:
- first_name: Rupert
  full_name: Frank, Rupert L
  last_name: Frank
- first_name: Élliott
  full_name: Lieb, Élliott H
  last_name: Lieb
- first_name: Robert
  full_name: Robert Seiringer
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Frank R, Lieb É, Seiringer R. Hardy-Lieb-Thirring inequalities for fractional
    Schrödinger operators. <i>Journal of the American Mathematical Society</i>. 2008;21(4):925-950.
    doi:<a href="https://doi.org/10.1090/S0894-0347-07-00582-6">10.1090/S0894-0347-07-00582-6</a>
  apa: Frank, R., Lieb, É., &#38; Seiringer, R. (2008). Hardy-Lieb-Thirring inequalities
    for fractional Schrödinger operators. <i>Journal of the American Mathematical
    Society</i>. American Mathematical Society. <a href="https://doi.org/10.1090/S0894-0347-07-00582-6">https://doi.org/10.1090/S0894-0347-07-00582-6</a>
  chicago: Frank, Rupert, Élliott Lieb, and Robert Seiringer. “Hardy-Lieb-Thirring
    Inequalities for Fractional Schrödinger Operators.” <i>Journal of the American
    Mathematical Society</i>. American Mathematical Society, 2008. <a href="https://doi.org/10.1090/S0894-0347-07-00582-6">https://doi.org/10.1090/S0894-0347-07-00582-6</a>.
  ieee: R. Frank, É. Lieb, and R. Seiringer, “Hardy-Lieb-Thirring inequalities for
    fractional Schrödinger operators,” <i>Journal of the American Mathematical Society</i>,
    vol. 21, no. 4. American Mathematical Society, pp. 925–950, 2008.
  ista: Frank R, Lieb É, Seiringer R. 2008. Hardy-Lieb-Thirring inequalities for fractional
    Schrödinger operators. Journal of the American Mathematical Society. 21(4), 925–950.
  mla: Frank, Rupert, et al. “Hardy-Lieb-Thirring Inequalities for Fractional Schrödinger
    Operators.” <i>Journal of the American Mathematical Society</i>, vol. 21, no.
    4, American Mathematical Society, 2008, pp. 925–50, doi:<a href="https://doi.org/10.1090/S0894-0347-07-00582-6">10.1090/S0894-0347-07-00582-6</a>.
  short: R. Frank, É. Lieb, R. Seiringer, Journal of the American Mathematical Society
    21 (2008) 925–950.
date_created: 2018-12-11T11:57:19Z
date_published: 2008-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:07Z
day: '01'
doi: 10.1090/S0894-0347-07-00582-6
extern: 1
intvolume: '        21'
issue: '4'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/math/0610593
month: '01'
oa: 1
page: 925 - 950
publication: Journal of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '4546'
quality_controlled: 0
status: public
title: Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators
type: journal_article
volume: 21
year: '2008'
...
---
_id: '2380'
abstract:
- lang: eng
  text: The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed
    attention as a description of fermionic gases interacting with local pairwise
    interactions. We present here a rigorous analysis of the BCS functional for general
    pair interaction potentials. For both zero and positive temperature, we show that
    the existence of a non-trivial solution of the nonlinear BCS gap equation is equivalent
    to the existence of a negative eigenvalue of a certain linear operator. From this
    we conclude the existence of a critical temperature below which the BCS pairing
    wave function does not vanish identically. For attractive potentials, we prove
    that the critical temperature is non-zero and exponentially small in the strength
    of the potential.
author:
- first_name: Christian
  full_name: Hainzl, Christian
  last_name: Hainzl
- first_name: Eman
  full_name: Hamza, Eman
  last_name: Hamza
- first_name: Robert
  full_name: Robert Seiringer
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
- first_name: Jan
  full_name: Solovej, Jan P
  last_name: Solovej
citation:
  ama: Hainzl C, Hamza E, Seiringer R, Solovej J. The BCS functional for general pair
    interactions. <i>Communications in Mathematical Physics</i>. 2008;281(2):349-367.
    doi:<a href="https://doi.org/10.1007/s00220-008-0489-2">10.1007/s00220-008-0489-2</a>
  apa: Hainzl, C., Hamza, E., Seiringer, R., &#38; Solovej, J. (2008). The BCS functional
    for general pair interactions. <i>Communications in Mathematical Physics</i>.
    Springer. <a href="https://doi.org/10.1007/s00220-008-0489-2">https://doi.org/10.1007/s00220-008-0489-2</a>
  chicago: Hainzl, Christian, Eman Hamza, Robert Seiringer, and Jan Solovej. “The
    BCS Functional for General Pair Interactions.” <i>Communications in Mathematical
    Physics</i>. Springer, 2008. <a href="https://doi.org/10.1007/s00220-008-0489-2">https://doi.org/10.1007/s00220-008-0489-2</a>.
  ieee: C. Hainzl, E. Hamza, R. Seiringer, and J. Solovej, “The BCS functional for
    general pair interactions,” <i>Communications in Mathematical Physics</i>, vol.
    281, no. 2. Springer, pp. 349–367, 2008.
  ista: Hainzl C, Hamza E, Seiringer R, Solovej J. 2008. The BCS functional for general
    pair interactions. Communications in Mathematical Physics. 281(2), 349–367.
  mla: Hainzl, Christian, et al. “The BCS Functional for General Pair Interactions.”
    <i>Communications in Mathematical Physics</i>, vol. 281, no. 2, Springer, 2008,
    pp. 349–67, doi:<a href="https://doi.org/10.1007/s00220-008-0489-2">10.1007/s00220-008-0489-2</a>.
  short: C. Hainzl, E. Hamza, R. Seiringer, J. Solovej, Communications in Mathematical
    Physics 281 (2008) 349–367.
date_created: 2018-12-11T11:57:20Z
date_published: 2008-07-01T00:00:00Z
date_updated: 2021-01-12T06:57:08Z
day: '01'
doi: 10.1007/s00220-008-0489-2
extern: 1
intvolume: '       281'
issue: '2'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/math-ph/0703086
month: '07'
oa: 1
page: 349 - 367
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4547'
quality_controlled: 0
status: public
title: The BCS functional for general pair interactions
type: journal_article
volume: 281
year: '2008'
...
---
_id: '2381'
abstract:
- lang: eng
  text: We determine the sharp constant in the Hardy inequality for fractional Sobolev
    spaces. To do so, we develop a non-linear and non-local version of the ground
    state representation, which even yields a remainder term. From the sharp Hardy
    inequality we deduce the sharp constant in a Sobolev embedding which is optimal
    in the Lorentz scale. In the appendix, we characterize the cases of equality in
    the rearrangement inequality in fractional Sobolev spaces.
author:
- first_name: Rupert
  full_name: Frank, Rupert L
  last_name: Frank
- first_name: Robert
  full_name: Robert Seiringer
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Frank R, Seiringer R. Non-linear ground state representations and sharp Hardy
    inequalities. <i>Journal of Functional Analysis</i>. 2008;255(12):3407-3430. doi:<a
    href="https://doi.org/10.1016/j.jfa.2008.05.015">10.1016/j.jfa.2008.05.015</a>
  apa: Frank, R., &#38; Seiringer, R. (2008). Non-linear ground state representations
    and sharp Hardy inequalities. <i>Journal of Functional Analysis</i>. Academic
    Press. <a href="https://doi.org/10.1016/j.jfa.2008.05.015">https://doi.org/10.1016/j.jfa.2008.05.015</a>
  chicago: Frank, Rupert, and Robert Seiringer. “Non-Linear Ground State Representations
    and Sharp Hardy Inequalities.” <i>Journal of Functional Analysis</i>. Academic
    Press, 2008. <a href="https://doi.org/10.1016/j.jfa.2008.05.015">https://doi.org/10.1016/j.jfa.2008.05.015</a>.
  ieee: R. Frank and R. Seiringer, “Non-linear ground state representations and sharp
    Hardy inequalities,” <i>Journal of Functional Analysis</i>, vol. 255, no. 12.
    Academic Press, pp. 3407–3430, 2008.
  ista: Frank R, Seiringer R. 2008. Non-linear ground state representations and sharp
    Hardy inequalities. Journal of Functional Analysis. 255(12), 3407–3430.
  mla: Frank, Rupert, and Robert Seiringer. “Non-Linear Ground State Representations
    and Sharp Hardy Inequalities.” <i>Journal of Functional Analysis</i>, vol. 255,
    no. 12, Academic Press, 2008, pp. 3407–30, doi:<a href="https://doi.org/10.1016/j.jfa.2008.05.015">10.1016/j.jfa.2008.05.015</a>.
  short: R. Frank, R. Seiringer, Journal of Functional Analysis 255 (2008) 3407–3430.
date_created: 2018-12-11T11:57:20Z
date_published: 2008-12-15T00:00:00Z
date_updated: 2021-01-12T06:57:08Z
day: '15'
doi: 10.1016/j.jfa.2008.05.015
extern: 1
intvolume: '       255'
issue: '12'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/0803.0503
month: '12'
oa: 1
page: 3407 - 3430
publication: Journal of Functional Analysis
publication_status: published
publisher: Academic Press
publist_id: '4543'
quality_controlled: 0
status: public
title: Non-linear ground state representations and sharp Hardy inequalities
type: journal_article
volume: 255
year: '2008'
...
---
_id: '2382'
abstract:
- lang: eng
  text: We show that the Lieb-Liniger model for one-dimensional bosons with repulsive
    δ-function interaction can be rigorously derived via a scaling limit from a dilute
    three-dimensional Bose gas with arbitrary repulsive interaction potential of finite
    scattering length. For this purpose, we prove bounds on both the eigenvalues and
    corresponding eigenfunctions of three-dimensional bosons in strongly elongated
    traps and relate them to the corresponding quantities in the Lieb-Liniger model.
    In particular, if both the scattering length a and the radius r of the cylindrical
    trap go to zero, the Lieb-Liniger model with coupling constant g ∼ a/r 2 is derived.
    Our bounds are uniform in g in the whole parameter range 0 ≤ g ≤ ∞, and apply
    to the Hamiltonian for three-dimensional bosons in a spectral window of size ∼
    r -2 above the ground state energy.
author:
- first_name: Robert
  full_name: Robert Seiringer
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
- first_name: Jun
  full_name: Yin, Jun
  last_name: Yin
citation:
  ama: Seiringer R, Yin J. The Lieb-Liniger model as a limit of dilute bosons in three
    dimensions. <i>Communications in Mathematical Physics</i>. 2008;284(2):459-479.
    doi:<a href="https://doi.org/10.1007/s00220-008-0521-6">10.1007/s00220-008-0521-6</a>
  apa: Seiringer, R., &#38; Yin, J. (2008). The Lieb-Liniger model as a limit of dilute
    bosons in three dimensions. <i>Communications in Mathematical Physics</i>. Springer.
    <a href="https://doi.org/10.1007/s00220-008-0521-6">https://doi.org/10.1007/s00220-008-0521-6</a>
  chicago: Seiringer, Robert, and Jun Yin. “The Lieb-Liniger Model as a Limit of Dilute
    Bosons in Three Dimensions.” <i>Communications in Mathematical Physics</i>. Springer,
    2008. <a href="https://doi.org/10.1007/s00220-008-0521-6">https://doi.org/10.1007/s00220-008-0521-6</a>.
  ieee: R. Seiringer and J. Yin, “The Lieb-Liniger model as a limit of dilute bosons
    in three dimensions,” <i>Communications in Mathematical Physics</i>, vol. 284,
    no. 2. Springer, pp. 459–479, 2008.
  ista: Seiringer R, Yin J. 2008. The Lieb-Liniger model as a limit of dilute bosons
    in three dimensions. Communications in Mathematical Physics. 284(2), 459–479.
  mla: Seiringer, Robert, and Jun Yin. “The Lieb-Liniger Model as a Limit of Dilute
    Bosons in Three Dimensions.” <i>Communications in Mathematical Physics</i>, vol.
    284, no. 2, Springer, 2008, pp. 459–79, doi:<a href="https://doi.org/10.1007/s00220-008-0521-6">10.1007/s00220-008-0521-6</a>.
  short: R. Seiringer, J. Yin, Communications in Mathematical Physics 284 (2008) 459–479.
date_created: 2018-12-11T11:57:21Z
date_published: 2008-12-01T00:00:00Z
date_updated: 2021-01-12T06:57:08Z
day: '01'
doi: 10.1007/s00220-008-0521-6
extern: 1
intvolume: '       284'
issue: '2'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/0709.4022
month: '12'
oa: 1
page: 459 - 479
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4544'
quality_controlled: 0
status: public
title: The Lieb-Liniger model as a limit of dilute bosons in three dimensions
type: journal_article
volume: 284
year: '2008'
...
---
_id: '2383'
abstract:
- lang: eng
  text: We study the relativistic electron-positron field at positive temperature
    in the Hartree-Fock approximation. We consider both the case with and without
    exchange terms, and investigate the existence and properties of minimizers. Our
    approach is non-perturbative in the sense that the relevant electron subspace
    is determined in a self-consistent way. The present work is an extension of previous
    work by Hainzl, Lewin, Séré and Solovej where the case of zero temperature was
    considered.
author:
- first_name: Christian
  full_name: Hainzl, Christian
  last_name: Hainzl
- first_name: Mathieu
  full_name: Lewin, Mathieu
  last_name: Lewin
- first_name: Robert
  full_name: Robert Seiringer
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Hainzl C, Lewin M, Seiringer R. A nonlinear model for relativistic electrons
    at positive temperature. <i>Reviews in Mathematical Physics</i>. 2008;20(10):1283-1307.
    doi:<a href="https://doi.org/10.1142/S0129055X08003547">10.1142/S0129055X08003547</a>
  apa: Hainzl, C., Lewin, M., &#38; Seiringer, R. (2008). A nonlinear model for relativistic
    electrons at positive temperature. <i>Reviews in Mathematical Physics</i>. World
    Scientific Publishing. <a href="https://doi.org/10.1142/S0129055X08003547">https://doi.org/10.1142/S0129055X08003547</a>
  chicago: Hainzl, Christian, Mathieu Lewin, and Robert Seiringer. “A Nonlinear Model
    for Relativistic Electrons at Positive Temperature.” <i>Reviews in Mathematical
    Physics</i>. World Scientific Publishing, 2008. <a href="https://doi.org/10.1142/S0129055X08003547">https://doi.org/10.1142/S0129055X08003547</a>.
  ieee: C. Hainzl, M. Lewin, and R. Seiringer, “A nonlinear model for relativistic
    electrons at positive temperature,” <i>Reviews in Mathematical Physics</i>, vol.
    20, no. 10. World Scientific Publishing, pp. 1283–1307, 2008.
  ista: Hainzl C, Lewin M, Seiringer R. 2008. A nonlinear model for relativistic electrons
    at positive temperature. Reviews in Mathematical Physics. 20(10), 1283–1307.
  mla: Hainzl, Christian, et al. “A Nonlinear Model for Relativistic Electrons at
    Positive Temperature.” <i>Reviews in Mathematical Physics</i>, vol. 20, no. 10,
    World Scientific Publishing, 2008, pp. 1283–307, doi:<a href="https://doi.org/10.1142/S0129055X08003547">10.1142/S0129055X08003547</a>.
  short: C. Hainzl, M. Lewin, R. Seiringer, Reviews in Mathematical Physics 20 (2008)
    1283–1307.
date_created: 2018-12-11T11:57:21Z
date_published: 2008-11-01T00:00:00Z
date_updated: 2021-01-12T06:57:09Z
day: '01'
doi: 10.1142/S0129055X08003547
extern: 1
intvolume: '        20'
issue: '10'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/0802.4054
month: '11'
oa: 1
page: 1283 - 1307
publication: Reviews in Mathematical Physics
publication_status: published
publisher: World Scientific Publishing
publist_id: '4545'
quality_controlled: 0
status: public
title: A nonlinear model for relativistic electrons at positive temperature
type: journal_article
volume: 20
year: '2008'
...
---
_id: '2415'
alternative_title:
- Contemporary Mathematics
author:
- first_name: Uli
  full_name: Uli Wagner
  id: 36690CA2-F248-11E8-B48F-1D18A9856A87
  last_name: Wagner
  orcid: 0000-0002-1494-0568
citation:
  ama: 'Wagner U. k-Sets and k-facets. In: Goodman J, Pach J, Pollack R, eds. <i>Surveys
    on Discrete and Computational Geometry: Twenty Years Later</i>. Vol 453. American
    Mathematical Society; 2008:443-514. doi:<a href="https://doi.org/10.1090/conm/453">10.1090/conm/453</a>'
  apa: 'Wagner, U. (2008). k-Sets and k-facets. In J. Goodman, J. Pach, &#38; R. Pollack
    (Eds.), <i>Surveys on Discrete and Computational Geometry: Twenty Years Later</i>
    (Vol. 453, pp. 443–514). American Mathematical Society. <a href="https://doi.org/10.1090/conm/453">https://doi.org/10.1090/conm/453</a>'
  chicago: 'Wagner, Uli. “K-Sets and k-Facets.” In <i>Surveys on Discrete and Computational
    Geometry: Twenty Years Later</i>, edited by Jacob Goodman, János Pach, and Richard
    Pollack, 453:443–514. American Mathematical Society, 2008. <a href="https://doi.org/10.1090/conm/453">https://doi.org/10.1090/conm/453</a>.'
  ieee: 'U. Wagner, “k-Sets and k-facets,” in <i>Surveys on Discrete and Computational
    Geometry: Twenty Years Later</i>, vol. 453, J. Goodman, J. Pach, and R. Pollack,
    Eds. American Mathematical Society, 2008, pp. 443–514.'
  ista: 'Wagner U. 2008.k-Sets and k-facets. In: Surveys on Discrete and Computational
    Geometry: Twenty Years Later. Contemporary Mathematics, vol. 453, 443–514.'
  mla: 'Wagner, Uli. “K-Sets and k-Facets.” <i>Surveys on Discrete and Computational
    Geometry: Twenty Years Later</i>, edited by Jacob Goodman et al., vol. 453, American
    Mathematical Society, 2008, pp. 443–514, doi:<a href="https://doi.org/10.1090/conm/453">10.1090/conm/453</a>.'
  short: 'U. Wagner, in:, J. Goodman, J. Pach, R. Pollack (Eds.), Surveys on Discrete
    and Computational Geometry: Twenty Years Later, American Mathematical Society,
    2008, pp. 443–514.'
date_created: 2018-12-11T11:57:32Z
date_published: 2008-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:21Z
day: '01'
doi: 10.1090/conm/453
editor:
- first_name: Jacob
  full_name: Goodman, Jacob E
  last_name: Goodman
- first_name: János
  full_name: Pach, János
  last_name: Pach
- first_name: Richard
  full_name: Pollack, Richard
  last_name: Pollack
extern: 1
intvolume: '       453'
month: '01'
page: 443 - 514
publication: 'Surveys on Discrete and Computational Geometry: Twenty Years Later'
publication_status: published
publisher: American Mathematical Society
publist_id: '4510'
quality_controlled: 0
status: public
title: k-Sets and k-facets
type: book_chapter
volume: 453
year: '2008'
...
---
_id: '2432'
abstract:
- lang: eng
  text: We study the disk containment problem introduced by Neumann-Lara and Urrutia
    and its generalization to higher dimensions. We relate the problem to centerpoints
    and lower centerpoints of point sets. Moreover, we show that for any set of n
    points in ℝd, there is a subset A ⊆ S of size [d+3/2] such that any ball containing
    A contains at least roughly 4/5ed 3n points of S. This improves previous bounds
    for which the constant was exponentially small in d. We also consider a generalization
    of the planar disk containment problem to families of pseudodisks.
alternative_title:
- LNCS
author:
- first_name: Shakhar
  full_name: Smorodinsky, Shakhar
  last_name: Smorodinsky
- first_name: Marek
  full_name: Sulovský, Marek
  last_name: Sulovský
- first_name: Uli
  full_name: Uli Wagner
  id: 36690CA2-F248-11E8-B48F-1D18A9856A87
  last_name: Wagner
  orcid: 0000-0002-1494-0568
citation:
  ama: 'Smorodinsky S, Sulovský M, Wagner U. On center regions and balls containing
    many points. In: Vol 5092. Springer; 2008:363-373. doi:<a href="https://doi.org/10.1007/978-3-540-69733-6_36">10.1007/978-3-540-69733-6_36</a>'
  apa: 'Smorodinsky, S., Sulovský, M., &#38; Wagner, U. (2008). On center regions
    and balls containing many points (Vol. 5092, pp. 363–373). Presented at the COCOON:
    Conference on Computing and Combinatorics, Springer. <a href="https://doi.org/10.1007/978-3-540-69733-6_36">https://doi.org/10.1007/978-3-540-69733-6_36</a>'
  chicago: Smorodinsky, Shakhar, Marek Sulovský, and Uli Wagner. “On Center Regions
    and Balls Containing Many Points,” 5092:363–73. Springer, 2008. <a href="https://doi.org/10.1007/978-3-540-69733-6_36">https://doi.org/10.1007/978-3-540-69733-6_36</a>.
  ieee: 'S. Smorodinsky, M. Sulovský, and U. Wagner, “On center regions and balls
    containing many points,” presented at the COCOON: Conference on Computing and
    Combinatorics, 2008, vol. 5092, pp. 363–373.'
  ista: 'Smorodinsky S, Sulovský M, Wagner U. 2008. On center regions and balls containing
    many points. COCOON: Conference on Computing and Combinatorics, LNCS, vol. 5092,
    363–373.'
  mla: Smorodinsky, Shakhar, et al. <i>On Center Regions and Balls Containing Many
    Points</i>. Vol. 5092, Springer, 2008, pp. 363–73, doi:<a href="https://doi.org/10.1007/978-3-540-69733-6_36">10.1007/978-3-540-69733-6_36</a>.
  short: S. Smorodinsky, M. Sulovský, U. Wagner, in:, Springer, 2008, pp. 363–373.
conference:
  name: 'COCOON: Conference on Computing and Combinatorics'
date_created: 2018-12-11T11:57:38Z
date_published: 2008-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:27Z
day: '01'
doi: 10.1007/978-3-540-69733-6_36
extern: 1
intvolume: '      5092'
month: '01'
page: 363 - 373
publication_status: published
publisher: Springer
publist_id: '4482'
quality_controlled: 0
status: public
title: On center regions and balls containing many points
type: conference
volume: 5092
year: '2008'
...