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Title: Mathematical aspects of the Kubo formula for electrical conductivity with dissipation
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.  more » « less
Award ID(s):
1922165
PAR ID:
10472339
Author(s) / Creator(s):
; ;
Publisher / Repository:
Springer
Date Published:
Journal Name:
Japan Journal of Industrial and Applied Mathematics
Volume:
40
Issue:
3
ISSN:
0916-7005
Page Range / eLocation ID:
1765 to 1795
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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