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...
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| Date: | 2005 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2005
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| Series: | Український математичний журнал |
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/165745 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Quantum-Classical Wigner-Liouville Equation / R. Kapral, A. Sergi // Український математичний журнал. — 2005. — Т. 57, № 6. — С. 749–756. — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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