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Quantum Nonlinear Dynamics of Continuously Measured Systems

By A. J. Scott and Gerard J. Milburn

Abstract

Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and classical nonlinear dynamics. Previous solutions have focussed on computing quantities associated with a statistical ensemble such as variance or entropy. However a more direct comparison would compare classical predictions to the quantum for continuous simultaneous measurement of position and momentum of a single system. In this paper we give a theory of such measurement and show that chaotic behaviour in classical systems can be reproduced by continuously measured quantum systems

Topics: Classical mechanics, Hilbert spaces, Nonlinear-dynamical systems, Quantum-theory, Measurement, 230113 Dynamical Systems
Year: 2000
OAI identifier: oai:espace.library.uq.edu.au:UQ:11165

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