@article{1198, abstract = {We consider a model of fermions interacting via point interactions, defined via a certain weighted Dirichlet form. While for two particles the interaction corresponds to infinite scattering length, the presence of further particles effectively decreases the interaction strength. We show that the model becomes trivial in the thermodynamic limit, in the sense that the free energy density at any given particle density and temperature agrees with the corresponding expression for non-interacting particles.}, author = {Moser, Thomas and Seiringer, Robert}, issn = {03779017}, journal = {Letters in Mathematical Physics}, number = {3}, pages = { 533 -- 552}, publisher = {Springer}, title = {{Triviality of a model of particles with point interactions in the thermodynamic limit}}, doi = {10.1007/s11005-016-0915-x}, volume = {107}, year = {2017}, } @article{997, abstract = {Recently it was shown that molecules rotating in superfluid helium can be described in terms of the angulon quasiparticles (Phys. Rev. Lett. 118, 095301 (2017)). Here we demonstrate that in the experimentally realized regime the angulon can be seen as a point charge on a 2-sphere interacting with a gauge field of a non-abelian magnetic monopole. Unlike in several other settings, the gauge fields of the angulon problem emerge in the real coordinate space, as opposed to the momentum space or some effective parameter space. Furthermore, we find a topological transition associated with making the monopole abelian, which takes place in the vicinity of the previously reported angulon instabilities. These results pave the way for studying topological phenomena in experiments on molecules trapped in superfluid helium nanodroplets, as well as on other realizations of orbital impurity problems.}, author = {Yakaboylu, Enderalp and Deuchert, Andreas and Lemeshko, Mikhail}, issn = {0031-9007}, journal = {Physical Review Letters}, number = {23}, publisher = {American Physical Society}, title = {{Emergence of non-abelian magnetic monopoles in a quantum impurity problem}}, doi = {10.1103/PhysRevLett.119.235301}, volume = {119}, year = {2017}, } @article{1143, abstract = {We study the ground state of a dilute Bose gas in a scaling limit where the Gross-Pitaevskii functional emerges. This is a repulsive nonlinear Schrödinger functional whose quartic term is proportional to the scattering length of the interparticle interaction potential. We propose a new derivation of this limit problem, with a method that bypasses some of the technical difficulties that previous derivations had to face. The new method is based on a combination of Dyson\'s lemma, the quantum de Finetti theorem and a second moment estimate for ground states of the effective Dyson Hamiltonian. It applies equally well to the case where magnetic fields or rotation are present.}, author = {Nam, Phan and Rougerie, Nicolas and Seiringer, Robert}, journal = {Analysis and PDE}, number = {2}, pages = {459 -- 485}, publisher = {Mathematical Sciences Publishers}, title = {{Ground states of large bosonic systems: The gross Pitaevskii limit revisited}}, doi = {10.2140/apde.2016.9.459}, volume = {9}, year = {2016}, } @article{1620, abstract = {We consider the Bardeen–Cooper–Schrieffer free energy functional for particles interacting via a two-body potential on a microscopic scale and in the presence of weak external fields varying on a macroscopic scale. We study the influence of the external fields on the critical temperature. We show that in the limit where the ratio between the microscopic and macroscopic scale tends to zero, the next to leading order of the critical temperature is determined by the lowest eigenvalue of the linearization of the Ginzburg–Landau equation.}, author = {Frank, Rupert and Hainzl, Christian and Seiringer, Robert and Solovej, Jan}, journal = {Communications in Mathematical Physics}, number = {1}, pages = {189 -- 216}, publisher = {Springer}, title = {{The external field dependence of the BCS critical temperature}}, doi = {10.1007/s00220-015-2526-2}, volume = {342}, year = {2016}, } @article{1622, abstract = {We prove analogues of the Lieb–Thirring and Hardy–Lieb–Thirring inequalities for many-body quantum systems with fractional kinetic operators and homogeneous interaction potentials, where no anti-symmetry on the wave functions is assumed. These many-body inequalities imply interesting one-body interpolation inequalities, and we show that the corresponding one- and many-body inequalities are actually equivalent in certain cases.}, author = {Lundholm, Douglas and Nam, Phan and Portmann, Fabian}, journal = {Archive for Rational Mechanics and Analysis}, number = {3}, pages = {1343 -- 1382}, publisher = {Springer}, title = {{Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems}}, doi = {10.1007/s00205-015-0923-5}, volume = {219}, year = {2016}, } @article{1436, abstract = {We study the time evolution of a system of N spinless fermions in R3 which interact through a pair potential, e.g., the Coulomb potential. We compare the dynamics given by the solution to Schrödinger's equation with the time-dependent Hartree-Fock approximation, and we give an estimate for the accuracy of this approximation in terms of the kinetic energy of the system. This leads, in turn, to bounds in terms of the initial total energy of the system.}, author = {Bach, Volker and Breteaux, Sébastien and Petrat, Sören P and Pickl, Peter and Tzaneteas, Tim}, journal = {Journal de Mathématiques Pures et Appliquées}, number = {1}, pages = {1 -- 30}, publisher = {Elsevier}, title = {{Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction}}, doi = {10.1016/j.matpur.2015.09.003}, volume = {105}, year = {2016}, } @article{1478, abstract = {We consider the Tonks-Girardeau gas subject to a random external potential. If the disorder is such that the underlying one-particle Hamiltonian displays localization (which is known to be generically the case), we show that there is exponential decay of correlations in the many-body eigenstates. Moreover, there is no Bose-Einstein condensation and no superfluidity, even at zero temperature.}, author = {Seiringer, Robert and Warzel, Simone}, journal = {New Journal of Physics}, number = {3}, publisher = {IOP Publishing Ltd.}, title = {{Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas}}, doi = {10.1088/1367-2630/18/3/035002}, volume = {18}, year = {2016}, } @article{1486, abstract = {We review recent results concerning the mathematical properties of the Bardeen-Cooper-Schrieffer (BCS) functional of superconductivity, which were obtained in a series of papers, partly in collaboration with R. Frank, E. Hamza, S. Naboko, and J. P. Solovej. Our discussion includes, in particular, an investigation of the critical temperature for a general class of interaction potentials, as well as a study of its dependence on external fields. We shall explain how the Ginzburg-Landau model can be derived from the BCS theory in a suitable parameter regime.}, author = {Hainzl, Christian and Seiringer, Robert}, journal = {Journal of Mathematical Physics}, number = {2}, publisher = {American Institute of Physics}, title = {{The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties}}, doi = {10.1063/1.4941723}, volume = {57}, year = {2016}, } @article{1491, abstract = {We study the ground state of a trapped Bose gas, starting from the full many-body Schrödinger Hamiltonian, and derive the non-linear Schrödinger energy functional in the limit of a large particle number, when the interaction potential converges slowly to a Dirac delta function. Our method is based on quantitative estimates on the discrepancy between the full many-body energy and its mean-field approximation using Hartree states. These are proved using finite dimensional localization and a quantitative version of the quantum de Finetti theorem. Our approach covers the case of attractive interactions in the regime of stability. In particular, our main new result is a derivation of the 2D attractive non-linear Schrödinger ground state.}, author = {Lewin, Mathieu and Nam, Phan and Rougerie, Nicolas}, journal = {Transactions of the American Mathematical Society}, number = {9}, pages = {6131 -- 6157}, publisher = {American Mathematical Society}, title = {{The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases}}, doi = {10.1090/tran/6537}, volume = {368}, year = {2016}, } @article{1493, abstract = {We introduce a new method for deriving the time-dependent Hartree or Hartree-Fock equations as an effective mean-field dynamics from the microscopic Schrödinger equation for fermionic many-particle systems in quantum mechanics. The method is an adaption of the method used in Pickl (Lett. Math. Phys. 97 (2) 151–164 2011) for bosonic systems to fermionic systems. It is based on a Gronwall type estimate for a suitable measure of distance between the microscopic solution and an antisymmetrized product state. We use this method to treat a new mean-field limit for fermions with long-range interactions in a large volume. Some of our results hold for singular attractive or repulsive interactions. We can also treat Coulomb interaction assuming either a mild singularity cutoff or certain regularity conditions on the solutions to the Hartree(-Fock) equations. In the considered limit, the kinetic and interaction energy are of the same order, while the average force is subleading. For some interactions, we prove that the Hartree(-Fock) dynamics is a more accurate approximation than a simpler dynamics that one would expect from the subleading force. With our method we also treat the mean-field limit coupled to a semiclassical limit, which was discussed in the literature before, and we recover some of the previous results. All results hold for initial data close (but not necessarily equal) to antisymmetrized product states and we always provide explicit rates of convergence.}, author = {Petrat, Sören P and Pickl, Peter}, journal = {Mathematical Physics, Analysis and Geometry}, number = {1}, publisher = {Springer}, title = {{A new method and a new scaling for deriving fermionic mean-field dynamics}}, doi = {10.1007/s11040-016-9204-2}, volume = {19}, year = {2016}, } @article{1545, abstract = {We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our sufficient conditions are optimal in the sense that they become necessary when the relevant one-body operators commute.}, author = {Nam, Phan and Napiórkowski, Marcin M and Solovej, Jan}, journal = {Journal of Functional Analysis}, number = {11}, pages = {4340 -- 4368}, publisher = {Academic Press}, title = {{Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations}}, doi = {10.1016/j.jfa.2015.12.007}, volume = {270}, year = {2016}, } @article{1422, abstract = {We study the time-dependent Bogoliubov–de-Gennes equations for generic translation-invariant fermionic many-body systems. For initial states that are close to thermal equilibrium states at temperatures near the critical temperature, we show that the magnitude of the order parameter stays approximately constant in time and, in particular, does not follow a time-dependent Ginzburg–Landau equation, which is often employed as a phenomenological description and predicts a decay of the order parameter in time. The full non-linear structure of the equations is necessary to understand this behavior.}, author = {Frank, Rupert and Hainzl, Christian and Schlein, Benjamin and Seiringer, Robert}, journal = {Letters in Mathematical Physics}, number = {7}, pages = {913 -- 923}, publisher = {Springer}, title = {{Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations}}, doi = {10.1007/s11005-016-0847-5}, volume = {106}, year = {2016}, } @inproceedings{1428, abstract = {We report on a mathematically rigorous analysis of the superfluid properties of a Bose- Einstein condensate in the many-body ground state of a one-dimensional model of interacting bosons in a random potential.}, author = {Könenberg, Martin and Moser, Thomas and Seiringer, Robert and Yngvason, Jakob}, booktitle = {Journal of Physics: Conference Series}, location = {Shanghai, China}, number = {1}, publisher = {IOP Publishing Ltd.}, title = {{Superfluidity and BEC in a Model of Interacting Bosons in a Random Potential}}, doi = {10.1088/1742-6596/691/1/012016}, volume = {691}, year = {2016}, } @article{1259, abstract = {We consider the Bogolubov–Hartree–Fock functional for a fermionic many-body system with two-body interactions. For suitable interaction potentials that have a strong enough attractive tail in order to allow for two-body bound states, but are otherwise sufficiently repulsive to guarantee stability of the system, we show that in the low-density limit the ground state of this model consists of a Bose–Einstein condensate of fermion pairs. The latter can be described by means of the Gross–Pitaevskii energy functional.}, author = {Bräunlich, Gerhard and Hainzl, Christian and Seiringer, Robert}, journal = {Mathematical Physics, Analysis and Geometry}, number = {2}, publisher = {Springer}, title = {{Bogolubov–Hartree–Fock theory for strongly interacting fermions in the low density limit}}, doi = {10.1007/s11040-016-9209-x}, volume = {19}, year = {2016}, } @article{1267, abstract = {We give a simplified proof of the nonexistence of large nuclei in the liquid drop model and provide an explicit bound. Our bound is within a factor of 2.3 of the conjectured value and seems to be the first quantitative result.}, author = {Frank, Rupert and Killip, Rowan and Nam, Phan}, journal = {Letters in Mathematical Physics}, number = {8}, pages = {1033 -- 1036}, publisher = {Springer}, title = {{Nonexistence of large nuclei in the liquid drop model}}, doi = {10.1007/s11005-016-0860-8}, volume = {106}, year = {2016}, } @article{1291, abstract = {We consider Ising models in two and three dimensions, with short range ferromagnetic and long range, power-law decaying, antiferromagnetic interactions. We let J be the ratio between the strength of the ferromagnetic to antiferromagnetic interactions. The competition between these two kinds of interactions induces the system to form domains of minus spins in a background of plus spins, or vice versa. If the decay exponent p of the long range interaction is larger than d + 1, with d the space dimension, this happens for all values of J smaller than a critical value Jc(p), beyond which the ground state is homogeneous. In this paper, we give a characterization of the infinite volume ground states of the system, for p > 2d and J in a left neighborhood of Jc(p). In particular, we prove that the quasi-one-dimensional states consisting of infinite stripes (d = 2) or slabs (d = 3), all of the same optimal width and orientation, and alternating magnetization, are infinite volume ground states. Our proof is based on localization bounds combined with reflection positivity.}, author = {Giuliani, Alessandro and Seiringer, Robert}, journal = {Communications in Mathematical Physics}, number = {3}, pages = {983 -- 1007}, publisher = {Springer}, title = {{Periodic striped ground states in Ising models with competing interactions}}, doi = {10.1007/s00220-016-2665-0}, volume = {347}, year = {2016}, } @article{1704, abstract = {Given a convex function (Formula presented.) and two hermitian matrices A and B, Lewin and Sabin study in (Lett Math Phys 104:691–705, 2014) the relative entropy defined by (Formula presented.). Among other things, they prove that the so-defined quantity is monotone if and only if (Formula presented.) is operator monotone. The monotonicity is then used to properly define (Formula presented.) for bounded self-adjoint operators acting on an infinite-dimensional Hilbert space by a limiting procedure. More precisely, for an increasing sequence of finite-dimensional projections (Formula presented.) with (Formula presented.) strongly, the limit (Formula presented.) is shown to exist and to be independent of the sequence of projections (Formula presented.). The question whether this sequence converges to its "obvious" limit, namely (Formula presented.), has been left open. We answer this question in principle affirmatively and show that (Formula presented.). If the operators A and B are regular enough, that is (A − B), (Formula presented.) and (Formula presented.) are trace-class, the identity (Formula presented.) holds.}, author = {Deuchert, Andreas and Hainzl, Christian and Seiringer, Robert}, journal = {Letters in Mathematical Physics}, number = {10}, pages = {1449 -- 1466}, publisher = {Springer}, title = {{Note on a family of monotone quantum relative entropies}}, doi = {10.1007/s11005-015-0787-5}, volume = {105}, year = {2015}, } @article{1807, abstract = {We study a double Cahn-Hilliard type functional related to the Gross-Pitaevskii energy of two-components Bose-Einstein condensates. In the case of large but same order intercomponent and intracomponent coupling strengths, we prove Γ-convergence to a perimeter minimisation functional with an inhomogeneous surface tension. We study the asymptotic behavior of the surface tension as the ratio between the intercomponent and intracomponent coupling strengths becomes very small or very large and obtain good agreement with the physical literature. We obtain as a consequence, symmetry breaking of the minimisers for the harmonic potential.}, author = {Goldman, Michael and Royo-Letelier, Jimena}, journal = {ESAIM - Control, Optimisation and Calculus of Variations}, number = {3}, pages = {603 -- 624}, publisher = {EDP Sciences}, title = {{Sharp interface limit for two components Bose-Einstein condensates}}, doi = {10.1051/cocv/2014040}, volume = {21}, year = {2015}, } @article{1880, abstract = {We investigate the relation between Bose-Einstein condensation (BEC) and superfluidity in the ground state of a one-dimensional model of interacting bosons in a strong random potential. We prove rigorously that in a certain parameter regime the superfluid fraction can be arbitrarily small while complete BEC prevails. In another regime there is both complete BEC and complete superfluidity, despite the strong disorder}, author = {Könenberg, Martin and Moser, Thomas and Seiringer, Robert and Yngvason, Jakob}, journal = {New Journal of Physics}, publisher = {IOP Publishing Ltd.}, title = {{Superfluid behavior of a Bose-Einstein condensate in a random potential}}, doi = {10.1088/1367-2630/17/1/013022}, volume = {17}, year = {2015}, } @article{2085, abstract = {We study the spectrum of a large system of N identical bosons interacting via a two-body potential with strength 1/N. In this mean-field regime, Bogoliubov's theory predicts that the spectrum of the N-particle Hamiltonian can be approximated by that of an effective quadratic Hamiltonian acting on Fock space, which describes the fluctuations around a condensed state. Recently, Bogoliubov's theory has been justified rigorously in the case that the low-energy eigenvectors of the N-particle Hamiltonian display complete condensation in the unique minimizer of the corresponding Hartree functional. In this paper, we shall justify Bogoliubov's theory for the high-energy part of the spectrum of the N-particle Hamiltonian corresponding to (non-linear) excited states of the Hartree functional. Moreover, we shall extend the existing results on the excitation spectrum to the case of non-uniqueness and/or degeneracy of the Hartree minimizer. In particular, the latter covers the case of rotating Bose gases, when the rotation speed is large enough to break the symmetry and to produce multiple quantized vortices in the Hartree minimizer. }, author = {Nam, Phan and Seiringer, Robert}, journal = {Archive for Rational Mechanics and Analysis}, number = {2}, pages = {381 -- 417}, publisher = {Springer}, title = {{Collective excitations of Bose gases in the mean-field regime}}, doi = {10.1007/s00205-014-0781-6}, volume = {215}, year = {2015}, }