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Inflow boundary conditions for the time dependent one-dimensional Schrödinger equation. (English. Abridged French version) Zbl 1158.35344

A transient quantum model for one-dimensional charge transport is derived and shown to lead in the semiclassical limit to the Vlasov equation with inflow boundary conditions. Asymptotic formulae involving quantum reflection-transmission coefficients and time delays are used to construct a hybrid model coupling quantum descriptions to kinetic ones in a time-dependent one-dimensional setting.

MSC:

35J10 Schrödinger operator, Schrödinger equation
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
35Q40 PDEs in connection with quantum mechanics
82D10 Statistical mechanics of plasmas
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