2,548 research outputs found
Theories of Linear Response in BCS Superfluids and How They Meet Fundamental Constraints
We address the importance of symmetry and symmetry breaking on linear
response theories of fermionic BCS superfluids. The linear theory of a
noninteracting Fermi gas is reviewed and several consistency constraints are
verified. The challenge to formulate linear response theories of BCS
superfluids consistent with density and spin conservation laws comes from the
presence of a broken U(1) symmetry associated with
electromagnetism (EM) and we discuss two routes for circumventing this. The
first route follows Nambu's integral-equation approach for the EM vertex
function, but this method is not specific for BCS superfluids. We focus on the
second route based on a consistent-fluctuation-of-the order-parameter (CFOP)
approach where the gauge transformation and the fluctuations of the order
parameter are treated on equal footing. The CFOP approach allows one to
explicitly verify several important constraints: The EM vertex satisfies not
only a Ward identity which guarantees charge conservation but also a -limit
Ward identity associated with the compressibility sum rule. In contrast, the
spin degrees of freedom associated with another U(1) symmetry are not
affected by the Cooper-pair condensation that breaks only the
U(1) symmetry. As a consequence the collective modes from the
fluctuations of the order parameter only couple to the density response
function but decouple from the spin response function, which reflects the
different fates of the two U(1) symmetries in the superfluid phase. Our
formulation lays the ground work for application to more general theories of
BCS-Bose Einstein Condensation crossover both above and below .Comment: Review on gauge invariance and charge-spin difference of BCS theory.
27 pages, 1 figure. Some typos have been correcte
Shear Viscosity of Uniform Fermi Gases with Population Imbalance
The shear viscosity plays an important role in studies of transport phenomena
in ultracold Fermi gases and serves as a diagnostic of various microscopic
theories. Due to the complicated phase structures of population-imbalanced
Fermi gases, past works mainly focus on unpolarized Fermi gases. Here we
investigate the shear viscosity of homogeneous, population-imbalanced Fermi
gases with tunable attractive interactions at finite temperatures by using a
pairing fluctuation theory for thermodynamical quantities and a gauge-invariant
linear response theory for transport coefficients. In the unitary and BEC
regimes, the shear viscosity increases with the polarization because the excess
majority fermions cause gapless excitations acting like a normal fluid. In the
weak BEC regime the excess fermions also suppress the noncondensed pairs at low
polarization, and we found a minimum in the ratio of shear viscosity and
relaxation time. To help constrain the relaxation time from linear response
theory, we derive an exact relation connecting some thermodynamic quantities
and transport coefficients at the mean-field level for unitary Fermi
superfluids with population imbalance. An approximate relation beyond
mean-field theory is proposed and only exhibits mild deviations from numerical
results.Comment: 11 pages, 4 figure
Fundamental Constraints on Linear Response Theories of Fermi Superfluids Above and Below
We present fundamental constraints required for a consistent linear response
theory of fermionic superfluids and address temperatures both above and below
the transition temperature . We emphasize two independent constraints, one
associated with gauge invariance (and the related Ward identity) and another
associated with the compressibility sum rule, both of which are satisfied in
strict BCS theory. However, we point out that it is the rare many body theory
which satisfies both of these. Indeed, well studied quantum Hall systems and
random-phase approximations to the electron gas are found to have difficulties
with meeting these constraints. We summarize two distinct theoretical
approaches which are, however, demonstrably compatible with gauge invariance
and the compressibility sum rule. The first of these involves an extension of
BCS theory to a mean field description of the BCS-Bose Einstein condensation
crossover. The second is the simplest Nozieres Schmitt- Rink (NSR) treatment of
pairing correlations in the normal state. As a point of comparison we focus on
the compressibility of each and contrast the predictions above .
We note here that despite the compliance with sum rules, this NSR based scheme
leads to an unphysical divergence in at the transition. Because of the
delicacy of the various consistency requirements, the results of this paper
suggest that avoiding this divergence may repair one problem while at the same
time introducing others.Comment: 13 pages, 2 figures. A review on gauge-invariant linear response
theories of BCS-BEC crossover and NSR theor
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