Generalized quantum Langevin equations for high-electric-field transport

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Two generalized quantum Langevin equations (GLE), one for the center-of-mass momentum and the other for the center-of-mass kinetic energy, are derived for an interacting system of electrons, impurities, and phonons. The GLEs are in their operator forms and the memory functions of momentum and energy directly reflect the nonlinear transport effects. When the GLEs are put into their macroscopic form by ensemble averaging, we obtain the momentum and energy transport equations by which the velocity fluctuation effects can be studied quantitatively. We find that the velocity fluctuations induce level broadening and reduce the overall mobility. A semiquantitative analysis shows that velocity fluctuation contributions to the transport equations gives results in good agreement with experiments on heterojunctions. © 1989 The American Physical Society.

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Physical Review B

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