## The Compressibility in Strongly Correlated Superconductors and Superfluids: From BCS to BEC    [PDF]

Hao Guo, Yan He, Chih-Chun Chien, K. Levin
We present a theoretical study of the compressibility, $\kappa$, in a Fermi gas with attractive contact interactions, providing predictions for the strongly-attractive regime and the superfluid phase. Our work emphasizes the compressibility sum rule and gauge invariance as constraints on $\kappa$ and we show how within a particular $t$-matrix approach, these can be satisfied in the normal phase when no approximations are made. For tractability, approximations must be introduced, and it is believed that thermodynamical approaches to $\kappa$ are more reliable, than correlation function based schemes. Contrasting with other studies in the literature, we present thermodynamic calculations of $\kappa$; these yield semi-quantitative agreement with experiment and provide physical insight into similar results obtained via quantum Monte Carlo simulations.
View original: http://arxiv.org/abs/1306.3189