A Correlation Estimate for Quantum Many-Body Systems at Positive Temperature

Abstract

We present an inequality that gives a lower bound on the expectation value of certain two-body interaction potentials in a general state on Fock space in terms of the corresponding expectation value for thermal equilibrium states of non-interacting systems and the difference in the free energy. This bound can be viewed as a rigorous version of first order perturbation theory for many-body systems at positive temperature. As an application, we give a proof of the first two terms in a high density (and high temperature) expansion of the free energy of jellium with Coulomb interactions, both in the fermionic and bosonic case. For bosons, our method works above the transition temperature (for the non-interacting gas) for Bose-Einstein condensation.

arXiv commentLaTeX, 25 pages; revised version, to appear in Rev. Math. Phys

References in corpus (2)

• Ground State Energy of the One-Component Charged Bose Gas
• The Thermodynamic Pressure of a Dilute Fermi Gas

Cited by in corpus (5)

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• Classical field theory limit of many-body quantum Gibbs states in 2D and 3D
• The free energy of the two-dimensional dilute Bose gas. I. Lower bound
• Symmetry breaking in the periodic Thomas--Fermi--Dirac--von Weizs{ä}cker model