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:1704.04819 · Journal of the European Mathematical Society

The excitation spectrum of Bose gases interacting through singular potentials

Chiara Boccato, Christian Brennecke, Serena Cenatiempo, Benjamin Schlein

Published Apr 22, 2020• 53 citations
arXivHTMLPDF

Abstract

We consider systems of N bosons in a box of volume one, interacting through a repulsive two-body potential of the form \kappa N^{3\beta-1} V(N^\beta x) . For all 0 < \beta < 1 , and for sufficiently small coupling constant \kappa > 0 , we establish the validity of Bogolyubov theory, identifying the ground state energy and the low-lying excitation spectrum up to errors that vanish in the limit of large N .

DOI
10.4171/jems/966

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

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

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

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

Cristina Caraci, Serena Cenatiempo, Benjamin Schlein

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 → ∞ .

arXiv:2205.12218•Annales Henri Poincaré•Mar 23, 2023•15 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

Bose–Einstein Condensation Beyond the Gross–Pitaevskii Regime

Arka Adhikari, Christian Brennecke, Benjamin Schlein

Abstract We consider N bosons in a box with volume one, interacting through a two-body potential with scattering length of the order $$N^{-1+\kappa }$$ N - 1 + κ , for $$\kappa >0$$ κ > 0 . Assuming that $$\kappa \in (0;1/43)$$ κ ∈ ( 0 ; 1 / 43 ) , we show that low-energy states exhibit Bose–Einstein condensation and we provide bounds on the expectation and on higher moments of the number of excitations.

arXiv:2002.03406•Annales Henri Poincaré•Dec 26, 2020•45 citations
We consider systems of N bosons in a box of volume one, interacting through a repulsive two-body potential of the form \kappa N^{3\beta-1} V(N^\beta x) . For all 0 < \beta < 1 , and for sufficiently small coupling constant \kappa > 0 , we establish the validity of Bogolyubov theory, identifying the ground state energy and the low-lying excitation spectrum up to errors that vanish in the limit of large N .
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.
Abstract We consider N bosons in a box with volume one, interacting through a two-body potential with scattering length of the order N−1+κN^{-1+\kappa }N−1+κ N - 1 + κ , for κ>0\kappa >0κ>0 κ > 0 . Assuming that κ∈(0;1/43)\kappa \in (0;1/43)κ∈(0;1/43) κ ∈ ( 0 ; 1 / 43 ) , we show that low-energy states exhibit Bose–Einstein condensation and we provide bounds on the expectation and on higher moments of the number of excitations.