Quantum-classical wigner-liouville equation
Quantum-classical wigner-liouville equation
Publication Type:
Journal ArticleSource:
Ukrainian Mathematical Journal, Volume 57, Number 6, p.891-899 (2005)URL:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-28844482627&doi=10.1007%2fs11253-005-0237-0&partnerID=40&md5=c55b221c10cd295bbf37ef8f31f5ce45Abstract:
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. © 2005 Springer Science+Business Media, Inc.
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