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A new second-order upper bound for the ground state energy of dilute Bose gases


Basti, Giulia; Cenatiempo, Serena; Schlein, Benjamin (2021). A new second-order upper bound for the ground state energy of dilute Bose gases. Forum of mathematics. Sigma, 9:e74.

Abstract

We establish an upper bound for the ground state energy per unit volume of a dilute Bose gas in the thermodynamic limit, capturing the correct second-order term, as predicted by the Lee–Huang–Yang formula. This result was first established in [20] by H.-T. Yau and J. Yin. Our proof, which applies to repulsive and compactly supported $V \in L^3 (\mathbb {R}^3)$, gives better rates and, in our opinion, is substantially simpler.

Abstract

We establish an upper bound for the ground state energy per unit volume of a dilute Bose gas in the thermodynamic limit, capturing the correct second-order term, as predicted by the Lee–Huang–Yang formula. This result was first established in [20] by H.-T. Yau and J. Yin. Our proof, which applies to repulsive and compactly supported $V \in L^3 (\mathbb {R}^3)$, gives better rates and, in our opinion, is substantially simpler.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Scopus Subject Areas:Physical Sciences > Analysis
Physical Sciences > Theoretical Computer Science
Physical Sciences > Algebra and Number Theory
Physical Sciences > Statistics and Probability
Physical Sciences > Mathematical Physics
Physical Sciences > Geometry and Topology
Physical Sciences > Discrete Mathematics and Combinatorics
Physical Sciences > Computational Mathematics
Uncontrolled Keywords:Computational Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics, Statistics and Probability, Algebra and Number Theory, Theoretical Computer Science, Analysis
Language:English
Date:1 January 2021
Deposited On:10 Jan 2022 14:02
Last Modified:26 Apr 2024 01:38
Publisher:Cambridge University Press
ISSN:2050-5094
OA Status:Gold
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1017/fms.2021.66
  • Content: Published Version
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)