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arXiv · 2304.04303

Mathematical aspects of the Kubo formula for electrical conductivity with dissipation

Alexander B. Watson·Dionisios Margetis·Mitchell Luskin
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Abstract

In this expository article, we present a systematic formal derivation of the Kubo formula for the linear-response current due to a time-harmonic electric field applied to non-interacting, spinless charged particles in a finite volume in the quantum setting. We model dissipation in a transparent way by assuming a sequence of scattering events occurring at random-time intervals modeled by a Poisson distribution. By taking the large-volume limit, we derive special cases of the formula for free electrons, continuum and tight-binding periodic systems, and the nearest-neighbor tight-binding model of graphene. We present the analogous formalism with dissipation to derive the Drude conductivity of classical free particles.

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Alexander B. Watson, Dionisios Margetis, Mitchell Luskin. 2023-04-09. Mathematical aspects of the Kubo formula for electrical conductivity with dissipation. https://arxiv.org/abs/2304.04303

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