Fock space construction of the quantum thermal flux operator

The construction of the flux operator in the Fock space of harmonic oscillator eigenfunctions is outlined. In one dimension, the flux operator is found to be F=(iω/√π) exp[−a+2/√2] [|1><0|−|0><1|] exp[−a2/2]. Two approaches for the temperature propagation are discussed, and the thermal flux eigenvalues for a double well potential are presented.