In this work we propose a hybrid Monte Carlo method for solving the Levinson equation. This equation describes the electron-phonon interaction on a quantum-kinetic level in a wire. The evolution problem becomes inhomogeneous due to the spatial dependence of the initial condition. The properties of the presented algorithm, such as computational complexity and accuracy, are investigated on the Grid by mixing quasi-random numbers and pseudo-random numbers. The numerical results are obtain for a physical model with GaAs material parameters in the case of zero electrical field.
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