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Advances in Condensed Matter Physics
Volume 2015 (2015), Article ID 582734, 9 pages
Research Article

Theoretical Approach to the Gauge Invariant Linear Response Theories for Ultracold Fermi Gases with Pseudogap

Hao Guo1 and Yan He2

1Department of Physics, Southeast University, Nanjing 211189, China
2College of Physical Science and Technology, Sichuan University, Chengdu, Sichuan 610064, China

Received 22 June 2015; Accepted 2 August 2015

Academic Editor: Artur P. Durajski

Copyright © 2015 Hao Guo and Yan He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Recent experimental progress allows for exploring some important physical quantities of ultracold Fermi gases, such as the compressibility, spin susceptibility, viscosity, optical conductivity, and spin diffusivity. Theoretically, these quantities can be evaluated from suitable linear response theories. For BCS superfluid, it has been found that the gauge invariant linear response theories can be fully consistent with some stringent consistency constraints. When the theory is generalized to stronger than BCS regime, one may meet serious difficulties to satisfy the gauge invariance conditions. In this paper, we try to construct density and spin linear response theories which are formally gauge invariant for a Fermi gas undergoing BCS-Bose-Einstein Condensation (BEC) crossover, especially below the superfluid transition temperature . We adapt a particular -matrix approach which is close to the formalism to incorporate noncondensed pairing in the normal state. We explicitly show that the fundamental constraints imposed by the Ward identities and -limit Ward identity are indeed satisfied.