Low-temperature expansion of the Casimir–Polder free energy for an atom interacting with a conductive plane

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 ∼ T 2 and comes from TM mode. The agreement of the expansion and exact expressions for different models of conductivity is numerically demonstrated.

The Casimir-Polder interaction of an atom and real graphene sheet: Verification of the Nernst heat theorem

“…The obtained result disagrees with Ref. 16. For a pristine graphene this work finds δ T F (a, T ) = C(a)T 3 at low T with no explicit expression for the coefficient C(a).…”

“…It is determined by a summation over the Matsubara frequencies of the zero-temperature part of the polarization tensor rather than by a dependence of this tensor on temperature as a parameter. Although our results are again in agreement with the Nernst heat theorem, they do not support the statement 16 that for the case ∆ > 2µ the leading term in the Casimir-Polder free energy vanishes with T exponentially fast.…”

“…The same expression with an explicitly determined coefficient C was, however, obtained earlier. 15 As to the case of gapped and doped graphene satisfying the condition ∆ > 2µ, it was concluded 16…”

The Low-Temperature Expansion of the Casimir-Polder Free Energy of an Atom with Graphene

“…It was shown in Ref. [23] that the low-temperature expansion reveals the unusual quadratic ∼ T 2 behavior. Next, detailed considerations [24,25] showed a more rich picture of low-temperature expansion depending on the relation between chemical potential µ and mass gap parameter m of the Dirac electron.…”

“…[19][20][21][22][23][24][25]. In the last few years, much attention has been given to the low-temperature expansion of the Casimir-Polder free energy for the atom/graphene system [7,[23][24][25]. In the case of an atom/ideal plane, the low-temperature correction to the Casimir-Polder free energy is proportional to the fourth degree of temperature ∼ T 4 .…”