The thermal gauge potentials in quantum transport

In this manuscript, we present another new thermal scalar and vector gauge potentials implemented by the quantum Boltzmann equation, which originates from the interaction of conduction electrons and phonons. To accomplish this task, we derive a temperature dependent four dimensional damping force by the Taylor series expansion on the self energy of the QBE, which can be related to the thermal scalar and vector gauge potentials, especially the fourth component of the damping force, which is just a power corresponding to a new scalar potential. Based on the local equilibrium assumption, we solve the QBE order by order using the Fourier transformation method. The temperature dependent damping force and other physical observables are exhibited in the figures, the higher of the temperature, the bigger of the damping force.