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Open Systems & Information Dynamics

The Role of a Second Reservoir in an Open BCS Model

Fabio Bagarello

Published Nov 11, 2005• 3 citations
Publisher

Abstract

In this paper we use the stochastic limit approach (SLA) in order to analyze some generalized versions of the open BCS model first introduced by Buffet and Martin and recently analyzed by the author using the SLA. In particular, considering different models, we discuss the role of a second reservoir interacting with the first one (but not with the system) in the computation of the critical temperature corresponding to the transition from a normal to a superconducting phase.

DOI
10.1007/s11080-005-4489-9

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In this paper we use the stochastic limit approach (SLA) in order to analyze some generalized versions of the open BCS model first introduced by Buffet and Martin and recently analyzed by the author using the SLA. In particular, considering different models, we discuss the role of a second reservoir interacting with the first one (but not with the system) in the computation of the critical temperature corresponding to the transition from a normal to a superconducting phase.
In papers devoted to superfluidity, the generally accepted statement that the dynamics of the corresponding phase transition is described by the stochastic model F or E can be frequently found. Nevertheless, the dynamical critical index has not been found even in the leading order of the perturbation theory. It is also unknown which model, E or F, in fact corresponds to this system. We use two different approaches to study this problem. First, we study the dynamics of the critical behavior in a neighborhood of the λ point using the renormalization group method based on a quantum microscopic model in the formalism of the time-dependent Green’s functions at a finite temperature. Second, we study the stochastic model F to find whether it is stable under compressibility effects. Both approaches lead to the same very unexpected result: the dynamics of the phase transition to the superfluid state are described by the stochastic model A with a known dynamical critical index.
We present dynamical equations that are valid in the vicinity of a phase transition to the superconducting state. In writing the equations, we take the possible influence of the magnetic interaction between charge carriers and temperature fluctuations into account. We discuss the type of the phase transition under study. We argue in favor of the applicability of stochastic dynamical model A according to the standard classification (the stochastic model with one two-component field without a conservation law) to describe the dynamics of this phase transition.