Dissipative canonical flows in classical and quantum mechanics

John Gough*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (SciVal)


A theory of stochastic flows over the algebra of observables of a dynamical system is presented in which the main objective is to ensure that the overall canonical/ symplectic structure on the algebra is preserved. We study both classical and quantum systems and the importance of physical interpretation in the Stratonovich interpretation is stressed. We find the natural formulation of quantum dissipative systems to be given in terms of quantum stochastic calculus. This treatment allows for a physically meaningful treatment of both constant and nonlinear dissipation. As an application, we quantize a mechanical system with the same nonlinear damping mechanism as the van der Pol oscillator.

Original languageEnglish
Pages (from-to)2805-2815
Number of pages11
JournalJournal of Mathematical Physics
Issue number6
Publication statusPublished - Jun 1999
Externally publishedYes


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