Quantum nonlinear dynamics of continuously measured systems

Details Quantum nonlinear dynamics of continuously measured systems Quantum nonlinear dynamics of continuously measured systems

2000-08-25

arxiv.org/abs/quant-ph/0008108v2

Phys. Rev. A 63, 042101 (2001)

Physics

Quantum Physics

11 pages, REVTEX, 3 figures

Scientific paper

10.1103/PhysRevA.63.042101

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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