a Correlation Estimate for Quantum ManyBody Systems at Positive Temperature
Abstract
We present an inequality that gives a lower bound on the expectation value of certain twobody interaction potentials in a general state on Fock space in terms of the corresponding expectation value for thermal equilibrium states of noninteracting systems and the difference in the free energy. This bound can be viewed as a rigorous version of firstorder perturbation theory for manybody 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 noninteracting gas) for BoseEinstein condensation.
 Publication:

Reviews in Mathematical Physics
 Pub Date:
 2006
 DOI:
 10.1142/S0129055X06002632
 arXiv:
 arXiv:mathph/0601051
 Bibcode:
 2006RvMaP..18..233S
 Keywords:

 Quantum manybody system;
 thermodynamic limit;
 jellium;
 quasifree states;
 correlation inequality;
 BoseEinstein condensation;
 Mathematical Physics;
 Mathematics  Mathematical Physics
 EPrint:
 LaTeX, 25 pages