Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2205.12218 · Annales Henri Poincaré

The Excitation Spectrum of Two-Dimensional Bose Gases in the Gross–Pitaevskii Regime

Cristina Caraci, Serena Cenatiempo, Benjamin Schlein

Published Mar 23, 2023• 15 citations
arXivHTMLPDF

Abstract

Abstract We consider a system of N bosons, in the two-dimensional unit torus. We assume particles to interact through a repulsive two-body potential, with a scattering length that is exponentially small in N (Gross–Pitaevskii regime). In this setting, we establish the validity of the predictions of Bogoliubov theory, determining the ground state energy of the Hamilton operator and its low-energy excitation spectrum, up to errors that vanish in the limit $$N \rightarrow \infty $$ N → ∞ .

DOI
10.1007/s00023-023-01278-1

Related papers

Bogoliubov theory in the Gross-Pitaevskii limit

Chiara Boccato, Christian Brennecke, Serena Cenatiempo +1 more

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 tends to infinity. Our results confirm Bogoliubov’s predictions.

•Jan 1, 2019•103 citations

Bogoliubov theory in the Gross–Pitaevskii limit

Chiara Boccato, Christian Brennecke, Serena Cenatiempo +1 more

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 the order N -1 (Gross-Pitaevskii regime).We determine the ground state energy and the lowenergy excitation spectrum, up to errors vanishing as N → ∞.Our results confirm Bogoliubov's predictions.

arXiv:1801.01389•Acta Mathematica•Jan 1, 2019•9 citations

Excitation spectrum of Bose gases beyond the Gross–Pitaevskii regime

Christian Brennecke, Marco Caporaletti, Benjamin Schlein

We consider Bose gases of [Formula: see text] particles in a box of volume one, interacting through a repulsive potential with scattering length of order [Formula: see text], for [Formula: see text]. Such regimes interpolate between the Gross–Pitaevskii and thermodynamic limits. Assuming that [Formula: see text] is sufficiently small, we determine the ground state energy and the low-energy excitation spectrum, up to errors vanishing in the limit [Formula: see text].

arXiv:2104.13003•Reviews in Mathematical Physics•Jun 4, 2022•29 citations

The excitation spectrum of the Bose gas in the Gross–Pitaevskii regime

Chiara Boccato

We consider a gas of interacting bosons trapped in a box of side length one in the Gross–Pitaevskii limit. We review the proof of the validity of Bogoliubov’s prediction for the ground state energy and the low-energy excitation spectrum. This note is based on joint work with C. Brennecke, S. Cenatiempo and B. Schlein.

arXiv:2001.00497•Reviews in Mathematical Physics•Mar 24, 2020•7 citations

Bose–Einstein Condensation for Two Dimensional Bosons in the Gross–Pitaevskii Regime

Cristina Caraci, Serena Cenatiempo, Benjamin Schlein

We consider systems of N bosons trapped on the two-dimensional unit torus, in the Gross-Pitaevskii regime, where the scattering length of the repulsive interaction is exponentially small in the number of particles. We show that low-energy states exhibit complete Bose-Einstein condensation, with almost optimal bounds on the number of orthogonal excitations.

arXiv:2011.05962•Journal of Statistical Physics•May 20, 2021•17 citations

BOGOLIUBOV EXCITATION SPECTRUM FOR BOSE–EINSTEIN CONDENSATES

Benjamin Schlein

We consider interacting Bose gases trapped in a box $Λ= [0;1]^3$ in the Gross-Pitaevskii limit. Assuming the potential to be weak enough, we establish the validity of Bogoliubov's prediction for the ground state energy and the low-energy excitation spectrum. These notes are based on \cite{BBCS3}, a joint work with C. Boccato, C. Brennecke and S. Cenatiempo.

arXiv:1802.06662•International Congress of Mathematicians (ICM)•May 1, 2019•3 citations
Abstract We consider a system of N bosons, in the two-dimensional unit torus. We assume particles to interact through a repulsive two-body potential, with a scattering length that is exponentially small in N (Gross–Pitaevskii regime). In this setting, we establish the validity of the predictions of Bogoliubov theory, determining the ground state energy of the Hamilton operator and its low-energy excitation spectrum, up to errors that vanish in the limit N→∞N \rightarrow \infty N→∞ N → ∞ .
We consider interacting Bose gases trapped in a box Λ=[0;1]3Λ= [0;1]^3Λ=[0;1]3 in the Gross-Pitaevskii limit. Assuming the potential to be weak enough, we establish the validity of Bogoliubov's prediction for the ground state energy and the low-energy excitation spectrum. These notes are based on \cite{BBCS3}, a joint work with C. Boccato, C. Brennecke and S. Cenatiempo.