Mathematical aspects of the Kubo formula for electrical conductivity with dissipation

被引：0
作者：
Alexander B. Watson
Dionisios Margetis
Mitchell Luskin
机构：
[1] University of Minnesota Twin Cities,Mathematics Department
[2] University of Maryland,Department of Mathematics, and Institute for Physical Science and Technology
来源：
Japan Journal of Industrial and Applied Mathematics | 2023年 / 40卷
关键词：
Kubo formula; Linear-response; Electrical conductivity; Dissipation; Trace formula; von Neumann equation; 78A25; 78A45; 81S05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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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页码：1765 / 1795
页数：30
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