Quantum dissipative effects in graphene-like mirrors

TL;DR

This paper investigates quantum dissipative effects caused by the accelerated motion of a graphene-like mirror, deriving a general expression for the effective action based on microscopic properties and analyzing dissipative phenomena.

Contribution

It introduces a general framework for calculating dissipative effects of moving graphene-like mirrors using vacuum polarization tensors and reflection coefficients.

Findings

Derived a general expression for the Euclidean effective action.

Identified contributions from TE and TM reflection coefficients.

Applied the framework to an accelerated graphene sheet model.

Abstract

We study quantum dissipative effects due to the accelerated motion of a single, imperfect, zero-width mirror. It is assumed that the microscopic degrees of freedom on the mirror are confined to it, like in plasma or graphene sheets. Therefore, the mirror is described by a vacuum polarization tensor $\Pi_{\alpha\beta}$ concentrated on a time-dependent surface. Under certain assumptions about the microscopic model for the mirror, we obtain a rather general expression for the Euclidean effective action, a functional of the time-dependent mirror's position, in terms of two invariants that characterize the tensor $\Pi_{\alpha\beta}$. The final result can be written in terms of the TE and TM reflection coefficients of the mirror, with qualitatively different contributions coming from them. We apply that general expression to derive the imaginary part of the `in-out' effective action, which measures dissipative effects induced by the mirror's motion, in different models, in particular for an accelerated graphene sheet.