A Stochastic Hamiltonian Approach for Quantum Jumps, Spontaneous Localizations, and Continuous Trajectories

Details A Stochastic Hamiltonian Approach for Quantum Jumps, Spontaneous Localizations, and Continuous Trajectories A Stochastic Hamiltonian Approach for Quantum Jumps, Spontaneous Localizations, and Continuous Trajectories

2005-12-22

arxiv.org/abs/quant-ph/0512192v1

Quantum Semiclass. Opt. 8 (1996) 167--187

Physics

Quantum Physics

32 pages. See also related papers at http://www.maths.nott.ac.uk/personal/vpb/vpb_publications.html and http://www.maths.not

Scientific paper

10.1088/1355-5111/8/1/013

We give an explicit stochastic Hamiltonian model of discontinuous unitary evolution for quantum spontaneous jumps like in a system of atoms in quantum optics, or in a system of quantum particles that interacts singularly with "bubbles" which admit a continual counting observation. This model allows to watch a quantum trajectory in a photodetector or in a cloud chamber by spontaneous localisations of the momentums of the scattered photons or bubbles. Thus, the continuous reduction and spontaneous localization theory is obtained from a Hamiltonian singular interaction as a result of quantum filtering, i.e., a sequential time continuous conditioning of an input quantum process by the output measurement data. We show that in the case of indistinguishable particles or atoms the a posteriori dynamics is mixing, giving rise to an irreversible Boltzmann-type reduction equation. The latter coincides with the nonstochastic Schroedinger equation only in the mean field approximation, whereas the central limit yelds Gaussian mixing fluctuations described by a quantum state reduction equation of diffusive type.

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