The low temperature behavior the Casimir-Polder energy for conductive plane

TL;DR

This paper investigates the low-temperature behavior of Casimir-Polder energy for a conductive plane, revealing a quadratic temperature correction primarily from TM modes, supported by numerical comparisons.

Contribution

It provides a general low-temperature expansion of Casimir-Polder energy for symmetric tensor conductivity, highlighting the dominant TM mode correction and validating it across models.

Findings

First correction proportional to T^2 from TM mode

Numerical agreement with exact models

Applicable to general symmetric tensor conductivity

Abstract

The low temperature expansion of the free energy of atom/plane system is considered for general symmetric form of tensor conductivity of the plane. It is shown that the first correction is proportional to second order of the temperature $\sim T^2$ and comes from TM mode. The agreement of the expansion and exact expressions for different models of conductivity is numerically demonstrated.