dorsal/arxiv
View SchemaA Stochastic Hamiltonian Approach for Quantum Jumps, Spontaneous Localizations, and Continuous Trajectories
| Authors | V. P. Belavkin, O. Melsheimer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512192 |
| URL | https://arxiv.org/abs/quant-ph/0512192 |
| DOI | 10.1088/1355-5111/8/1/013 |
| Journal | Quantum Semiclass. Opt. 8 (1996) 167--187 |
Abstract
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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"abstract": "We give an explicit stochastic Hamiltonian model of discontinuous unitary\nevolution for quantum spontaneous jumps like in a system of atoms in quantum\noptics, or in a system of quantum particles that interacts singularly with\n\"bubbles\" which admit a continual counting observation. This model allows to\nwatch a quantum trajectory in a photodetector or in a cloud chamber by\nspontaneous localisations of the momentums of the scattered photons or bubbles.\nThus, the continuous reduction and spontaneous localization theory is obtained\nfrom a Hamiltonian singular interaction as a result of quantum filtering, i.e.,\na sequential time continuous conditioning of an input quantum process by the\noutput measurement data. We show that in the case of indistinguishable\nparticles or atoms the a posteriori dynamics is mixing, giving rise to an\nirreversible Boltzmann-type reduction equation. The latter coincides with the\nnonstochastic Schroedinger equation only in the mean field approximation,\nwhereas the central limit yelds Gaussian mixing fluctuations described by a\nquantum state reduction equation of diffusive type.",
"arxiv_id": "quant-ph/0512192",
"authors": [
"V. P. Belavkin",
"O. Melsheimer"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1355-5111/8/1/013",
"journal_ref": "Quantum Semiclass. Opt. 8 (1996) 167--187",
"title": "A Stochastic Hamiltonian Approach for Quantum Jumps, Spontaneous Localizations, and Continuous Trajectories",
"url": "https://arxiv.org/abs/quant-ph/0512192"
},
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