dorsal/arxiv
View SchemaQuantum Flows as Markovian Limit of Emission, Absorption and Scattering Interactions
| Authors | John Gough |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0309056 |
| URL | https://arxiv.org/abs/quant-ph/0309056 |
| DOI | 10.1007/s00220-004-1163-y |
| Journal | Commun. Math. Phys. Vol. 254, no.2, 489-512, March 2005 |
Abstract
We consider a Markovian approximation, of weak coupling type, to an open system perturbation involving emission, absorption and scattering by reservoir quanta. The result is the general form for a quantum stochastic flow driven by creation, annihilation and gauge processes. A weak matrix limit is established for the convergence of the interaction-picture unitary to a unitary, adapted quantum stochastic process and of the Heisenberg dynamics to the corresponding quantum stochastic flow: the convergence strategy is similar to the quantum functional central limits introduced by Accardi, Frigerio and Lu$^{[ 1]}$. The principal terms in the Dyson series expansions are identified and re-summed after the limit to obtain explicit quantum stochastic differential equations with renormalized coefficients. An extension of the Pul\UNICODE{0xe9} inequalities$^{[ 2]}$ allows uniform estimates for the Dyson series expansion for both the unitary operator and the Heisenberg evolution to be obtained.
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"abstract": "We consider a Markovian approximation, of weak coupling type, to an open\nsystem perturbation involving emission, absorption and scattering by reservoir\nquanta. The result is the general form for a quantum stochastic flow driven by\ncreation, annihilation and gauge processes. A weak matrix limit is established\nfor the convergence of the interaction-picture unitary to a unitary, adapted\nquantum stochastic process and of the Heisenberg dynamics to the corresponding\nquantum stochastic flow: the convergence strategy is similar to the quantum\nfunctional central limits introduced by Accardi, Frigerio and Lu$^{[ 1]}$. The\nprincipal terms in the Dyson series expansions are identified and re-summed\nafter the limit to obtain explicit quantum stochastic differential equations\nwith renormalized coefficients. An extension of the Pul\\UNICODE{0xe9}\ninequalities$^{[ 2]}$ allows uniform estimates for the Dyson series expansion\nfor both the unitary operator and the Heisenberg evolution to be obtained.",
"arxiv_id": "quant-ph/0309056",
"authors": [
"John Gough"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/s00220-004-1163-y",
"journal_ref": "Commun. Math. Phys. Vol. 254, no.2, 489-512, March 2005",
"title": "Quantum Flows as Markovian Limit of Emission, Absorption and Scattering Interactions",
"url": "https://arxiv.org/abs/quant-ph/0309056"
},
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