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

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

2006-01-24

arxiv.org/abs/math-ph/0601051v2

Rev. Math. Phys. 18, 233 (2006)

Physics

Mathematical Physics

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

Scientific paper

10.1142/S0129055X06002632

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.

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