Field Theories for Ensembles with Temperature Inhomogeneities: Simple Non-interacting Fermionic/Bosonic Models with a Linear Temperature Gradient

We generalized a novel field theoretical framework treating temperature inhomogeneities systematically beyond linear response theory, to incorporate chemical potential inhomogeneities as well. We utilized a linear temperature profile and performed first-order perturbative calculations for effective 1D non-interacting lattice fermions. The new results on thermodynamic properties of Fermions show a dispersion relationship dependent on both the temperature gradient and space coordinates, which enters fermi distribution functions and local density of states. This shows contrast with bosons, whose dispersion relationship is not affected by the thermal inhomogeneities, despite a renormalized local particle density [1]. We also employed Non-Equilibrium Green’s Function formalism to investigate the transport properties upon the introduction of two leads connected to two ends of the wire. The results show an increase in thermal power and the breakdown of Widemann-Franz Law with an increasing temperature gradient, while the Widemann-Franz Law is restored in the linear response limit, as expected.



[1] Y. Gao and K.A. Muttalib, ``Non-equilibrium field theory with a temperature gradient: Thermal current in a nanowire'', Phys. Rev. B. 109, 155409 (2024).