Non-equilibrium Quantum Field Theory for Thermal Inhomogeneity in Thermoelectric Devices

We generalized the standard non-equilibrium field theory framework to incorporate a temperature gradient across a thermoelectric device. The framework uses a temperature-dependent pseudo-Hamiltonian generated from the exact density matrix in the presence of non-uniform temperatures. We proposed a perturbation theory for otherwise free particles with small temperature gradients in long wires and obtained the Fermi and Boson distribution functions to first order accuracy. In addition, non-linear thermal conductivity as a function of temperature difference is calculated. The framework should be adaptable to more general cases of temperature inhomogeneities in either fermionic or bosonic systems.