Quantum-Classical Wigner-Liouville Equation |
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Authors: | R Kapral A Sergi |
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Institution: | (1) University of Toronto, Toronto, Canada |
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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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Keywords: | |
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