Finite-temperature time-dependent effective theory for the Goldstone field in a BCS-type superfluid

Abstract

We extend to finite temperature the time-dependent effective theory for the Goldstone field ͑the phase of the pair field͒ which is appropriate for a superfluid containing one species of fermions with s-wave interactions, described by the BCS Lagrangian. We show that, when Landau damping is neglected, the effective theory can be written as a local time-dependent nonlinear Schrödinger Lagrangian which preserves the Galilean invariance of the zero-temperature effective theory and is identified with the superfluid component. We then calculate the relevant Landau terms that are nonlocal and that destroy the Galilean invariance. We show that the retarded propagator ͑in momentum space͒ can be well represented by two poles in the lower-half frequency plane, describing damping with a predicted temperature, frequency, and momentum dependence. It is argued that the real parts of the Landau terms can be approximately interpreted as contributing to the normal fluid component.

Effective action approach to the Leggett's mode in two-band superconductors

“…"normal" fluid component). This is the term responsible for the appearance of the Landau terms in the effective action [9,10].…”

“…For example, in [8] it was used to study the problem of the Galilean invariance of the effective Lagrangian at T = 0. The finite temperature time-dependent effective actions for the phase field in s-wave [9] and d-wave [10] neutral superconductors were derived addressing an old problem of time-dependent generalization of the GL theory. It is also convenient to investigate the plasma mode within this formalism taking into account the long-distance Coulomb repulsion between electrons [4,6] (see also more recent papers [11,12]).…”

Phase transition of trapped interacting Bose gases and the renormalization group

“…(25). In three spatial dimensions these RG equations have to be solved for ε = 1 together with the flow equation (24) of the grand thermodynamic potential.…”

“…The hat indicates that these quantities are Schwinger-Fock operators [23,24,25]. As in the homogeneous case, we now perform an expansion of (3) up to second order inĜ >Σ .…”

“…These quantities are to be interpreted as δ Y X(l) = δX(l)/δY (0), i.e., they describe the change δX(l) of a flow trajectory if the initial condition is changed infinitesimally by δY (0). If we write the flow equations (18) or (25) symbolically as …”