Non-Hamiltonian Commutators in Quantum Mechanics

Sergi, Alessandro (2005) Non-Hamiltonian Commutators in Quantum Mechanics. Physical Review E. (Submitted)

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Abstract

The symplectic structure of quantum commutators is first unveiled and then exploited to introduce generalized non-Hamiltonian brackets in quantum mechanics. It is easily recognized that quantum-classical systems are described by a particular realization of such a bracket. In light of previous work, this introduces a unified approach to classical and quantum-classical non-Hamiltonian dynamics. In order to illustrate the use of non-Hamiltonian commutators, it is shown how to define thermodynamic constraints in quantum-classical systems. In particular, quantum-classical Nos\'e-Hoover equations of motion and the associated stationary density matrix are derived. The non-Hamiltonian commutators for both Nos\'e-Hoover chains and Nos\'e-Andersen (constant-pressure constant temperature) dynamics are also given. Perspectives of the formalism are discussed.

Item Type: Other
Additional Information: Submitted to Physical Review E on August 8 2005
Subjects: M.U.S. - Contributi Scientifici > 01 - Scienze matematiche e informatiche
M.U.S. - Contributi Scientifici > 02 - Scienze fisiche
Depositing User: Dr Alessandro Sergi
Date Deposited: 14 Nov 2005
Last Modified: 13 Apr 2010 11:19
URI: http://cab.unime.it/mus/id/eprint/348

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