Nonlinear dynamical Casimir effect at weak nonstationarity

TL;DR

This paper investigates how small nonlinearities influence particle creation in the dynamical Casimir effect over long times, using effective Hamiltonian techniques and considering both field theory and quantum circuit analogs.

Contribution

It derives a resummed effective Hamiltonian accounting for loop corrections in a nonlinear dynamical Casimir effect setup, highlighting the significance of nonlinearities.

Findings

Loop corrections are comparable to tree-level particle production.

Nonlinearities significantly alter particle flux at large evolution times.

Resummation techniques reveal the importance of quantum corrections in the effect.

Abstract

We show that even small nonlinearities significantly affect particle production in the dynamical Casimir effect at large evolution times. To that end, we derive the effective Hamiltonian and resum leading loop corrections to the particle flux in a massless scalar field theory with time-dependent Dirichlet boundary conditions and quartic self-interaction. To perform the resummation, we assume small deviations from the equilibrium and employ a kind of rotating wave approximation. Besides that, we consider a quantum circuit analog of the dynamical Casimir effect, which is also essentially nonlinear. In both cases, loop contributions to the number of created particles are comparable to the tree-level values.