An Analysis of a Quantum Kinetic Two-band Model with Inflow Boundary Conditions

Chiara Manzini, Omar Morandi


We present a well-posedness study of a two-band envelope function model
in the Wigner formalism. It is obtained from a multiband Schrödinger-like system for the
conduction and the valence band envelope functions, derived by O.Morandi and M.Modugno, and
describes the mixed-states of an open quantum system. It consists of four coupled equations
for the unknown quasi-distribution functions. We include a non-linearly coupling with the Poisson
equation and consider the unknown functions defined in a one-dimensional, bounded spatial domain
with time-dependent ``inflow'' boundary conditions. We will prove the existence and uniqueness
of a global-in-time, classical solution.

[DOI: 10.1685/CSC06107] About DOI

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