2023/04/09 by Alexander Watson, Watson, Alexander B., Dionisios Margetis +3
Materials Science · Physics and Astronomy · #78 #81 #Electron and X-Ray Spectroscopy Techniques #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum and electron transport phenomena #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2304.04303
openalex publication_date 2023/04/09 · openalex created_date 2023/04/13 · openalex updated_date 2026/07/28
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.