Nonlocality as the source of purely quantum dynamics of BCS superconductors

TL;DR

This paper demonstrates that classical mean-field theory accurately describes local observables in far-from-equilibrium BCS superconductors in the thermodynamic limit, but global quantities reveal significant quantum fluctuations and nonthermal steady states.

Contribution

It provides an exact comparison between quantum and classical dynamics in BCS superconductors, highlighting the limits of mean-field approximation and revealing the nature of nonthermal steady states.

Findings

Mean field is exact for local observables in the thermodynamic limit.

Global quantities like entanglement entropy show breakdown of mean-field approximation.

The steady state is a gapless, nonthermal superconductor described by a generalized Gibbs ensemble.

Abstract

We show that the classical (mean-field) description of far from equilibrium superconductivity is exact in the thermodynamic limit for local observables but breaks down for global quantities, such as the entanglement entropy or Loschmidt echo. We do this by solving for and comparing exact quantum and exact classical long-time dynamics of a BCS superconductor with interaction strength inversely proportional to time and evaluating local observables explicitly. Mean field is exact for both normal and anomalous averages (superconducting order) in the thermodynamic limit. However, for anomalous expectation values, this limit does not commute with adiabatic and strong coupling limits and, as a consequence, their quantum fluctuations can be unusually strong. The long-time steady state of the system is a gapless superconductor whose superfluid properties are only accessible through energy resolved measurements. This state is nonthermal but conforms to an emergent generalized Gibbs ensemble. Our study clarifies the nature of symmetry-broken many-body states in and out of equilibrium and fills a crucial gap in the theory of time-dependent quantum integrability.