Lower bounds on the energy of the Bose gas

Abstract

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-Pitaevski length scale. The presentation includes both the 2 and 3 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.

arXiv commentWe corrected some typos and added some references

References in corpus (19)

• Ground State Energy of the Low Density Bose Gas
• The Second Order Upper Bound for the Ground Energy of a Bose Gas
• Ground State Energy of the Two-Component Charged Bose Gas
• Ground state energy of the two-dimensional weakly interacting Bose gas: First correction beyond Bogoliubov theory
• The ground state energy of a low density Bose gas: a second order upper bound
• Ground State Energy of the One-Component Charged Bose Gas
• Ground State Energy of the Low Density Fermi Gas
• Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime
• Dilute Bose gas in two dimensions: Density expansions and the Gross-Pitaevskii equation
• Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime
• The Mathematics of the Bose Gas and its Condensation
• Correlation Energy of a Weakly Interacting Fermi Gas
• The dilute Fermi gas via Bogoliubov theory
• A second order upper bound for the ground state energy of a hard-sphere gas in the Gross-Pitaevskii regime
• The excitation spectrum of two dimensional Bose gases in the Gross-Pitaevskii regime
• The Second Order Correction to the Ground State Energy of the Dilute Bose Gas
• The Bose gas in a box with Neumann boundary conditions
• The Gell-Mann$-$Brueckner Formula for the Correlation Energy of the Electron Gas: A Rigorous Upper Bound in the Mean-Field Regime
• Ground state energy of a dilute two-dimensional Bose gas from the Bogoliubov free energy functional

Cited by in corpus (1)

• A Short Proof of Bose-Einstein Condensation in the Gross-Pitaevskii Regime and Beyond