2020/04/28 by Kazuki Yamaga
Mathematics · Physics and Astronomy · #Adiabatic process #Conductivity #Dissipation #Dissipative system #Dynamics (music) #Fermion #Quantum #Quantum chaos and dynamical systems #Quantum many-body systems #Semigroup #Spectral Theory in Mathematical Physics #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.3390/axioms9040128
arxiv created 2020/04/28 · openalex created_date 2020/05/13 · openalex publication_date 2020/11/03 · arxiv updated 2020/12/02 · openalex updated_date 2026/08/05
In this paper, Non-Equilibrium Steady State that is induced by electric field and the conductivity of non-interacting fermion systems under the dissipative dynamics is discussed. The dissipation is taken into account within a framework of the quantum dynamical semigroup introduced by Davies (1977). We obtain a formula of the conductivity for the stationary state, which is applicable to arbitrary potentials. Our formula gives a justification of an adiabatic factor that is often introduced in practical calculation while using the Kubo formula. In addition, the conductivity of crystals (i.e., periodic potentials) is also discussed.