Free energy of a dilute Bose gas: Lower bound
Robert Seiringer
A lower bound is derived on the free energy (per unit volume) of a homogeneous Bose gas at density Q and temperature T. In the dilute regime, i.e., when a3 1, where a denotes the scattering length of the pair-interaction potential, our bound differs to leading order from the expression for non-interacting particles by the term 4πa(2 2}-[ - c]2+). Here, c(T) denotes the critical density for Bose-Einstein condensation (for the non-interacting gas), and [ · ]+ = max{ ·, 0} denotes the positive part. Our bound is uniform in the temperature up to temperatures of the order of the critical temperature, i.e., T ~ 2/3 or smaller. One of the key ingredients in the proof is the use of coherent states to extend the method introduced in [17] for estimating correlations to temperatures below the critical one.
Springer
2008
info:eu-repo/semantics/article
doc-type:article
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http://purl.org/coar/resource_type/c_6501
https://research-explorer.ista.ac.at/record/2374
Seiringer R. Free energy of a dilute Bose gas: Lower bound. <i>Communications in Mathematical Physics</i>. 2008;279(3):595-636. doi:<a href="https://doi.org/10.1007/s00220-008-0428-2">10.1007/s00220-008-0428-2</a>
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00220-008-0428-2
info:eu-repo/semantics/openAccess