---
_id: '7413'
abstract:
- lang: eng
text: We consider Bose gases consisting of N particles trapped in a box with volume
one and interacting through a repulsive potential with scattering length of order
N−1 (Gross–Pitaevskii regime). We determine the ground state energy and the low-energy
excitation spectrum, up to errors vanishing as N→∞. Our results confirm Bogoliubov’s
predictions.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Chiara
full_name: Boccato, Chiara
id: 342E7E22-F248-11E8-B48F-1D18A9856A87
last_name: Boccato
- first_name: Christian
full_name: Brennecke, Christian
last_name: Brennecke
- first_name: Serena
full_name: Cenatiempo, Serena
last_name: Cenatiempo
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
citation:
ama: Boccato C, Brennecke C, Cenatiempo S, Schlein B. Bogoliubov theory in the Gross–Pitaevskii
limit. Acta Mathematica. 2019;222(2):219-335. doi:10.4310/acta.2019.v222.n2.a1
apa: Boccato, C., Brennecke, C., Cenatiempo, S., & Schlein, B. (2019). Bogoliubov
theory in the Gross–Pitaevskii limit. Acta Mathematica. International Press
of Boston. https://doi.org/10.4310/acta.2019.v222.n2.a1
chicago: Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein.
“Bogoliubov Theory in the Gross–Pitaevskii Limit.” Acta Mathematica. International
Press of Boston, 2019. https://doi.org/10.4310/acta.2019.v222.n2.a1.
ieee: C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “Bogoliubov theory
in the Gross–Pitaevskii limit,” Acta Mathematica, vol. 222, no. 2. International
Press of Boston, pp. 219–335, 2019.
ista: Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2019. Bogoliubov theory in
the Gross–Pitaevskii limit. Acta Mathematica. 222(2), 219–335.
mla: Boccato, Chiara, et al. “Bogoliubov Theory in the Gross–Pitaevskii Limit.”
Acta Mathematica, vol. 222, no. 2, International Press of Boston, 2019,
pp. 219–335, doi:10.4310/acta.2019.v222.n2.a1.
short: C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Acta Mathematica 222
(2019) 219–335.
date_created: 2020-01-30T09:30:41Z
date_published: 2019-06-07T00:00:00Z
date_updated: 2023-09-06T15:24:31Z
day: '07'
department:
- _id: RoSe
doi: 10.4310/acta.2019.v222.n2.a1
external_id:
arxiv:
- '1801.01389'
isi:
- '000495865300001'
intvolume: ' 222'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1801.01389
month: '06'
oa: 1
oa_version: Preprint
page: 219-335
publication: Acta Mathematica
publication_identifier:
eissn:
- 1871-2509
issn:
- 0001-5962
publication_status: published
publisher: International Press of Boston
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bogoliubov theory in the Gross–Pitaevskii limit
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 222
year: '2019'
...
---
_id: '8494'
abstract:
- lang: eng
text: "We prove a form of Arnold diffusion in the a-priori stable case. Let\r\nH0(p)+ϵH1(θ,p,t),θ∈Tn,p∈Bn,t∈T=R/T,\r\nbe
a nearly integrable system of arbitrary degrees of freedom n⩾2 with a strictly
convex H0. We show that for a “generic” ϵH1, there exists an orbit (θ,p) satisfying\r\n∥p(t)−p(0)∥>l(H1)>0,\r\nwhere
l(H1) is independent of ϵ. The diffusion orbit travels along a codimension-1 resonance,
and the only obstruction to our construction is a finite set of additional resonances.\r\n\r\nFor
the proof we use a combination of geometric and variational methods, and manage
to adapt tools which have recently been developed in the a-priori unstable case."
article_processing_charge: No
article_type: original
author:
- first_name: Patrick
full_name: Bernard, Patrick
last_name: Bernard
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Ke
full_name: Zhang, Ke
last_name: Zhang
citation:
ama: Bernard P, Kaloshin V, Zhang K. Arnold diffusion in arbitrary degrees of freedom
and normally hyperbolic invariant cylinders. Acta Mathematica. 2016;217(1):1-79.
doi:10.1007/s11511-016-0141-5
apa: Bernard, P., Kaloshin, V., & Zhang, K. (2016). Arnold diffusion in arbitrary
degrees of freedom and normally hyperbolic invariant cylinders. Acta Mathematica.
Institut Mittag-Leffler. https://doi.org/10.1007/s11511-016-0141-5
chicago: Bernard, Patrick, Vadim Kaloshin, and Ke Zhang. “Arnold Diffusion in Arbitrary
Degrees of Freedom and Normally Hyperbolic Invariant Cylinders.” Acta Mathematica.
Institut Mittag-Leffler, 2016. https://doi.org/10.1007/s11511-016-0141-5.
ieee: P. Bernard, V. Kaloshin, and K. Zhang, “Arnold diffusion in arbitrary degrees
of freedom and normally hyperbolic invariant cylinders,” Acta Mathematica,
vol. 217, no. 1. Institut Mittag-Leffler, pp. 1–79, 2016.
ista: Bernard P, Kaloshin V, Zhang K. 2016. Arnold diffusion in arbitrary degrees
of freedom and normally hyperbolic invariant cylinders. Acta Mathematica. 217(1),
1–79.
mla: Bernard, Patrick, et al. “Arnold Diffusion in Arbitrary Degrees of Freedom
and Normally Hyperbolic Invariant Cylinders.” Acta Mathematica, vol. 217,
no. 1, Institut Mittag-Leffler, 2016, pp. 1–79, doi:10.1007/s11511-016-0141-5.
short: P. Bernard, V. Kaloshin, K. Zhang, Acta Mathematica 217 (2016) 1–79.
date_created: 2020-09-18T10:46:07Z
date_published: 2016-09-28T00:00:00Z
date_updated: 2021-01-12T08:19:39Z
day: '28'
doi: 10.1007/s11511-016-0141-5
extern: '1'
intvolume: ' 217'
issue: '1'
language:
- iso: eng
month: '09'
oa_version: None
page: 1-79
publication: Acta Mathematica
publication_identifier:
issn:
- 0001-5962
publication_status: published
publisher: Institut Mittag-Leffler
quality_controlled: '1'
status: public
title: Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant
cylinders
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 217
year: '2016'
...