Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross-Pitaevskii Regime

Abstract

We consider a translation-invariant system of $N$ bosons in ${\mathbb{T}}^3$ that interact through a repulsive two-body potential with scattering length of order $N^{-1}$ in the limit $N\to \infty$. We derive second order expressions for the one- and two-particle reduced density matrix matrices of the Gibbs state at fixed positive temperatures, thus obtaining a justification of Bogoliubov's prediction on the fluctuations around the condensate.

References in corpus (25)

• Proof of Bose-Einstein Condensation for Dilute Trapped Gases
• Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional
• Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases
• Ground State Energy of the Low Density Bose Gas
• Rigorous Derivation of the Gross-Pitaevskii Equation
• The excitation spectrum for weakly interacting bosons in a trap
• The Second Order Upper Bound for the Ground Energy of a Bose Gas
• The Excitation Spectrum for Weakly Interacting Bosons
• Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime
• Ground states of large bosonic systems: The gross-pitaevskii limit revisited
• Gross-Pitaevskii Dynamics for Bose-Einstein Condensates
• Complete Bose-Einstein condensation in the Gross-Pitaevskii regime
• Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime
• Optimal rate of condensation for trapped bosons in the Gross-Pitaevskii regime
• Bose-Einstein Condensation with Optimal Rate for Trapped Bosons in the Gross-Pitaevskii Regime
• Asymptotic expansion of low-energy excitations for weakly interacting bosons
• Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime
• Bose-Einstein Condensation in a Dilute, Trapped Gas at Positive Temperature
• Another proof of BEC in the GP-limit
• Gross-Pitaevskii Limit of a Homogeneous Bose Gas at Positive Temperature
• A second order upper bound for the ground state energy of a hard-sphere gas in the Gross-Pitaevskii regime
• The Bose gas in a box with Neumann boundary conditions
• The condensation of a trapped dilute Bose gas with three-body interactions
• Central Limit Theorem for Bose-Einstein Condensates
• Upper bound for the grand canonical free energy of the Bose gas in the Gross-Pitaevskii limit

Cited by in corpus (1)

• The excitation spectrum of a Bose gas with an impurity in the Gross-Pitaevskii regime