Temperature inhomogeneity in non-equilibrium field theory for electrons in a nanowire: thermodynamic and transport properties

Yuan Gao; K. A. Muttalib

doi:10.1016/j.aop.2025.169996

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arXiv · 2503.14778

Temperature inhomogeneity in non-equilibrium field theory for electrons in a nanowire: thermodynamic and transport properties

Yuan Gao·K. A. Muttalib

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Abstract

A nanowire with its two ends fixed at two different temperatures by external baths is the simplest example of a fermionic system with a temperature inhomogeneity, and could be an easy platform to study thermodynamic and transport properties of a boundary-driven open quantum system. Starting with a temperature-dependent pseudo free energy derived from an exact reduced density matrix and assuming a small temperature gradient $\gamma$ across the wire, we show within perturbation theory that electron dispersion relation and therefore the Fermi distribution becomes $\gamma$ and space coordinates dependent, leading to non-linear effects of the temperature inhomogeneity. In particular, we show that in the non-linear response regime, the Widemann-Franz Law for the ratio of thermal and electrical conductivities is generalized, and that the thermopower increases with increasing temperature gradient $\gamma$.

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Yuan Gao, K. A. Muttalib. 2025-03-18. Temperature inhomogeneity in non-equilibrium field theory for electrons in a nanowire: thermodynamic and transport properties. https://doi.org/10.1016/j.aop.2025.169996

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