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

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