Quantum-Classical Wigner-Liouville Equation
We consider a quantum system that is partitioned into a subsystem and a bath. Starting from the Wigner transform of the von Neumann equation for the quantum-mechanical density matrix of the entire system, the quantum-classical Wigner-Liouville equation is obtained in the limit where the masses M of...
Збережено в:
| Дата: | 2005 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2005
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/3641 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We consider a quantum system that is partitioned into a subsystem and a bath. Starting from the Wigner transform of the von Neumann equation for the quantum-mechanical density matrix of the entire system, the quantum-classical Wigner-Liouville equation is obtained in the limit where the masses M of the bath particles are large as compared with the masses m of the subsystem particles. The structure of this equation is discussed and it is shown how the abstract operator form of the quantum-classical Liouville equation is obtained by taking the inverse Wigner transform on the subsystem. Solutions in terms of classical trajectory segments and quantum transition or momentum jumps are described. |
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