Abstract
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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Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 6, pp. 749–756, June, 2005.
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Kapral, R., Sergi, A. Quantum-Classical Wigner-Liouville Equation. Ukr Math J 57, 891–899 (2005). https://doi.org/10.1007/s11253-005-0237-0
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DOI: https://doi.org/10.1007/s11253-005-0237-0