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Quantum nonlinear dynamics of continuously measured systems

A. J. Scott·G. J. Milburn
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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.

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A. J. Scott, G. J. Milburn. 2000-11-16. Quantum nonlinear dynamics of continuously measured systems. https://doi.org/10.1103/physreva.63.042101

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