Mathematical aspects of the Kubo formula for electrical conductivity with dissipation
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.
Keywords
Cite
@article{arxiv.2304.04303,
title = {Mathematical aspects of the Kubo formula for electrical conductivity with dissipation},
author = {Alexander B. Watson and Dionisios Margetis and Mitchell Luskin},
journal= {arXiv preprint arXiv:2304.04303},
year = {2023}
}
Comments
35 pages. Small corrections and improvements to exposition