Nonequilibrium Cooper pairing in the nonadiabatic regime

TL;DR

This paper provides a comprehensive analysis of the non-adiabatic dynamics of BCS superconductors, revealing integrable behavior, conserved quantities, and complex oscillations, with implications for understanding steady states in large systems.

Contribution

It offers an exact solution for the mean-field dynamics of Cooper pairing in the non-adiabatic regime, connecting quantum dynamics to classical integrable systems.

Findings

The dynamics reduce to a classical integrable Hamiltonian system.

The condensate exhibits irregular multi-frequency oscillations.

In the thermodynamic limit, the system approaches a steady state.

Abstract

We obtain a complete solution for the mean-field dynamics of the BCS paired state with a large, but finite number of Cooper pairs in the non-adiabatic regime. We show that the problem reduces to a classical integrable Hamiltonian system and derive a complete set of its integrals of motion. The condensate exhibits irregular multi-frequency oscillations ergodically exploring the part of the phase-space allowed by the conservation laws. In the thermodynamic limit however the system can asymptotically reach a steady state.