dorsal/arxiv
View SchemaGenuine quantum trajectories for non-Markovian processes
| Authors | Heinz-Peter Breuer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0403117 |
| URL | https://arxiv.org/abs/quant-ph/0403117 |
| DOI | 10.1103/PhysRevA.70.012106 |
| Journal | Phys. Rev. A 70, 012106 (2004) |
Abstract
A large class of non-Markovian quantum processes in open systems can be formulated through time-local master equations which are not in Lindblad form. It is shown that such processes can be embedded in a Markovian dynamics which involves a time dependent Lindblad generator on an extended state space. If the state space of the open system is given by some Hilbert space ${\mathcal{H}}$, the extended state space is the triple Hilbert space ${\mathcal{H}}\otimes{\mathbb C}^3$ which is obtained by combining the open system with a three state system. This embedding is used to derive an unraveling for non-Markovian time evolution by means of a stochastic process in the extended state space. The process is defined through a stochastic Schr\"odinger equation which generates genuine quantum trajectories for the state vector conditioned on a continuous monitoring of an environment. The construction leads to a continuous measurement interpretation for non-Markovian dynamics within the framework of the theory of quantum measurement.
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"abstract": "A large class of non-Markovian quantum processes in open systems can be\nformulated through time-local master equations which are not in Lindblad form.\nIt is shown that such processes can be embedded in a Markovian dynamics which\ninvolves a time dependent Lindblad generator on an extended state space. If the\nstate space of the open system is given by some Hilbert space ${\\mathcal{H}}$,\nthe extended state space is the triple Hilbert space\n${\\mathcal{H}}\\otimes{\\mathbb C}^3$ which is obtained by combining the open\nsystem with a three state system. This embedding is used to derive an\nunraveling for non-Markovian time evolution by means of a stochastic process in\nthe extended state space. The process is defined through a stochastic\nSchr\\\"odinger equation which generates genuine quantum trajectories for the\nstate vector conditioned on a continuous monitoring of an environment. The\nconstruction leads to a continuous measurement interpretation for non-Markovian\ndynamics within the framework of the theory of quantum measurement.",
"arxiv_id": "quant-ph/0403117",
"authors": [
"Heinz-Peter Breuer"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.70.012106",
"journal_ref": "Phys. Rev. A 70, 012106 (2004)",
"title": "Genuine quantum trajectories for non-Markovian processes",
"url": "https://arxiv.org/abs/quant-ph/0403117"
},
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