Derivation of nonlinear single-particle equations via many-body Lindblad superoperators: A density-matrix approach
| Autor: | Rosati, Roberto, Iotti, Rita Claudia, Dolcini, Fabrizio, Rossi, Fausto |
|---|---|
| Rok vydání: | 2014 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevB.90.125140 |
| Popis: | A recently proposed Markov approach provides Lindblad-type scattering superoperators, which ensure the physical (positive-definite) character of the many-body density matrix. We apply the mean-field approximation to such many-body equation, in the presence of one- and two-body scattering mechanisms, and we derive a closed equation of motion for the electronic single-particle density matrix, which turns out to be non-linear as well as non-Lindblad. We prove that, in spite of its nonlinear and non-Lindblad structure, the mean-field approximation does preserve the positive-definite character of the single-particle density matrix, an essential prerequisite of any reliable kinetic treatment of semiconductor quantum devices. This result is in striking contrast with conventional (non-Lindblad) Markov approaches, where the single-particle mean-field equations can lead to positivity violations and to unphysical results. Furthermore, the proposed single-particle formulation is extended to the case of quantum systems with spatial open boundaries, providing a formal derivation of a recently proposed density-matrix treatment based on a Lindblad-like system-reservoir scattering superoperator. Comment: 10 pages, 1 figure (submitted to Phys. Rev. B) |
| Databáze: | arXiv |
| Externí odkaz: |
|