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Beschreibung:
A one-dimensional coupled drift-diffusion dissipative Schrödinger model (hybrid model) is mathematically analyzed. The device domain is split into two parts: one in which the transport is well described by the drift-diffusion equations (classical zone) and another in which a quantum description via dissipative Schrödinger equations (quantum zone) is used. Both system are coupled such that the continuity of the current densities is guaranteed. The electrostatic potential is self-consistently determined by Poisson's equation on the whole device domain. We show that the hybrid model is well posed, and we prove existence of solutions and show their uniform boundedness, provided the distribution functions satisfy a so-called balance condition. The current densities are different from zero in the nonequilibrium case and are uniformly bounded.