TY - JOUR

T1 - Lower bounds on the energy of the Bose gas

AU - Fournais, Søren

AU - Girardot, Theotime

AU - Junge, Lukas

AU - Morin, Leo

AU - Olivieri, Marco

N1 - Publisher Copyright: © 2023 World Scientific Publishing Company.

PY - 2023

Y1 - 2023

N2 - We present an overview of the approach to establish a lower bound to the ground state energy for the dilute, interacting Bose gas in a periodic box. In this paper, the size of the box is larger than the Gross-Pitaevskii length scale. The presentation includes both the two-and three-dimensional cases, and catches the second-order correction, i.e.The Lee-Huang-Yang term. The calculation on a box of this length scale is the main step to calculate the energy in the thermodynamic limit. However, the periodic boundary condition simplifies many steps of the argument considerably compared to the localized problem coming from the thermodynamic case.

AB - We present an overview of the approach to establish a lower bound to the ground state energy for the dilute, interacting Bose gas in a periodic box. In this paper, the size of the box is larger than the Gross-Pitaevskii length scale. The presentation includes both the two-and three-dimensional cases, and catches the second-order correction, i.e.The Lee-Huang-Yang term. The calculation on a box of this length scale is the main step to calculate the energy in the thermodynamic limit. However, the periodic boundary condition simplifies many steps of the argument considerably compared to the localized problem coming from the thermodynamic case.

KW - Bogoliubov theory

KW - dilute Bose gases

KW - Lee-Huang-Yang formula

KW - Many-body quantum mechanics

UR - http://www.scopus.com/inward/record.url?scp=85172204805&partnerID=8YFLogxK

U2 - 10.1142/S0129055X23600048

DO - 10.1142/S0129055X23600048

M3 - Journal article

AN - SCOPUS:85172204805

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

SN - 0129-055X

M1 - 2360004

ER -