Casimir effect in the nonequilibrium steady-state of a quantum spin chain

TL;DR

This paper analytically calculates the Casimir force in a nonequilibrium quantum XX chain with energy flux, revealing a reduced force range due to suppressed fluctuations in the steady state.

Contribution

It provides a microscopics-based analytical calculation of the Casimir effect in a nonequilibrium quantum spin chain, a novel approach in this context.

Findings

Casimir force range is reduced out of equilibrium

Energy flux steady state suppresses fluctuations

Analytical results obtained for small transverse fields

Abstract

We present a fully microscopics-based calculation of the Casimir effect in a nonequilibrium system, namely an energy flux driven quantum XX chain. The force between the walls (transverse-field impurities) is calculated in a nonequilibrium steady state which is prepared by letting the system evolve from an initial state with the two halves of the chain prepared at equilibrium at different temperatures. The steady state emerging in the large-time limit is homogeneous but carries an energy flux. The Casimir force in this nonequilibrium state is calculated analytically in the limit when the transverse fields are small. We find that the the Casimir force range is reduced compared to the equilibrium case, and suggest that the reason for this is the reduction of fluctuations in the flux carrying steady state.