Phonon Coherent States in Nanomaterials

In our work we describe the heat transfer in nanomaterial by thermal excitations with accounting phonon coherent states. General second-quantization formalism for a time dependent problem for thermal conductivity is proposed. This method accounts both the usual phonon model of heat transfer and the formation of coherent Schrödinger states in each mode of the phonon system. An exact general form of solution with arbitrary initial conditions is analytically obtained. It is shown that at certain ratios of the interaction constants of phonons with the electronic subsystem a heat flow does not decay with time in the crystal that determines a heat superconductivity phenomenon