The energy of dilute Bose gases

Soren Fournais; Jan Philip Solovej

doi:10.4007/annals.2020.192.3.5

The energy of dilute Bose gases

Soren Fournais^*, Jan Philip Solovej

^*Corresponding author for this work

Department of Mathematical Sciences

Research output: Contribution to journal › Journal article › Research › peer-review

47 Citations (Scopus)

59 Downloads (Pure)

Abstract

For a dilute system of non-relativistic bosons interacting through a positive, compactly supported, L-1-potential v with scattering length a we prove that the ground state energy density satisfies the bound e(rho) >= 4 pi a rho(2)(1 + 128/15 root pi root rho a(3) + o(root rho a(3))), thereby proving the Lee-Huang-Yang formula for the energy density.

Original language	English
Journal	Annals of Mathematics
Volume	192
Issue number	3
Pages (from-to)	893-976
ISSN	0003-486X
DOIs	https://doi.org/10.4007/annals.2020.192.3.5
Publication status	Published - Nov 2020

Keywords

many-body quantum mechanics
dilute Bose gases
Bogolubov theory
Lee-Huang-Yang formula
GROUND-STATE ENERGY
EXCITATION SPECTRUM
INTERACTING BOSONS
ONE-COMPONENT

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10.4007/annals.2020.192.3.5

The energy of dilute Bose gaseAccepted author manuscript, 836 KBLicence: Other

Cite this

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title = "The energy of dilute Bose gases",

abstract = "For a dilute system of non-relativistic bosons interacting through a positive, compactly supported, L-1-potential v with scattering length a we prove that the ground state energy density satisfies the bound e(rho) >= 4 pi a rho(2)(1 + 128/15 root pi root rho a(3) + o(root rho a(3))), thereby proving the Lee-Huang-Yang formula for the energy density.",

keywords = "many-body quantum mechanics, dilute Bose gases, Bogolubov theory, Lee-Huang-Yang formula, GROUND-STATE ENERGY, EXCITATION SPECTRUM, INTERACTING BOSONS, ONE-COMPONENT",

author = "Soren Fournais and Solovej, {Jan Philip}",

year = "2020",

month = nov,

doi = "10.4007/annals.2020.192.3.5",

language = "English",

volume = "192",

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journal = "Annals of Mathematics",

issn = "0003-486X",

publisher = "Johns Hopkins University Press",

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TY - JOUR

T1 - The energy of dilute Bose gases

AU - Fournais, Soren

AU - Solovej, Jan Philip

PY - 2020/11

Y1 - 2020/11

N2 - For a dilute system of non-relativistic bosons interacting through a positive, compactly supported, L-1-potential v with scattering length a we prove that the ground state energy density satisfies the bound e(rho) >= 4 pi a rho(2)(1 + 128/15 root pi root rho a(3) + o(root rho a(3))), thereby proving the Lee-Huang-Yang formula for the energy density.

AB - For a dilute system of non-relativistic bosons interacting through a positive, compactly supported, L-1-potential v with scattering length a we prove that the ground state energy density satisfies the bound e(rho) >= 4 pi a rho(2)(1 + 128/15 root pi root rho a(3) + o(root rho a(3))), thereby proving the Lee-Huang-Yang formula for the energy density.

KW - many-body quantum mechanics

KW - dilute Bose gases

KW - Bogolubov theory

KW - Lee-Huang-Yang formula

KW - GROUND-STATE ENERGY

KW - EXCITATION SPECTRUM

KW - INTERACTING BOSONS

KW - ONE-COMPONENT

U2 - 10.4007/annals.2020.192.3.5

DO - 10.4007/annals.2020.192.3.5

M3 - Journal article

VL - 192

SP - 893

EP - 976

JO - Annals of Mathematics

JF - Annals of Mathematics

SN - 0003-486X

IS - 3

ER -