dorsal/arxiv
View SchemaA simple quantum equation for Decoherence and dissipation (through interaction with the environment)
| Authors | Erasmo Recami, Ruy H. A. Farias |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0206117 |
| URL | https://arxiv.org/abs/quant-ph/0206117 |
| DOI | 10.1393/ncb/i2009-10799-1 |
| Journal | Nuovo Cimento B147 (2009) 765-776 |
Abstract
Within the density matrix formalism, it is shown that a simple way to get decoherence is through the introduction of a "quantum" of time (chronon): which implies replacing the differential Liouville--von Neumann equation with a finite-difference version of it. In this way, one is given the possibility of using a rather simple quantum equation to describe the decoherence effects due to dissipation. Namely, the mere introduction (not of a "time-lattice", but simply) of a "chronon" allows us to go on from differential to finite-difference equations; and in particular to write down the quantum-theoretical equations (Schroedinger equation, Liouville--von Neumann equation,...) in three different ways: "retarded", "symmetrical", and "advanced". One of such three formulations --the retarded one-- describes in an elementary way a system which is exchanging (and losing) energy with the environment; and in its density-matrix version, indeed, it can be easily shown that all non-diagonal terms go to zero very rapidly. [A much larger presentation of the theoretical ground on which this paper is based appeared in the e-print quant-ph/9706059, and in the preprint IC/98/74, ICTP; Trieste, 1998].
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"abstract": "Within the density matrix formalism, it is shown that a simple way to get\ndecoherence is through the introduction of a \"quantum\" of time (chronon): which\nimplies replacing the differential Liouville--von Neumann equation with a\nfinite-difference version of it. In this way, one is given the possibility of\nusing a rather simple quantum equation to describe the decoherence effects due\nto dissipation. Namely, the mere introduction (not of a \"time-lattice\", but\nsimply) of a \"chronon\" allows us to go on from differential to\nfinite-difference equations; and in particular to write down the\nquantum-theoretical equations (Schroedinger equation, Liouville--von Neumann\nequation,...) in three different ways: \"retarded\", \"symmetrical\", and\n\"advanced\". One of such three formulations --the retarded one-- describes in an\nelementary way a system which is exchanging (and losing) energy with the\nenvironment; and in its density-matrix version, indeed, it can be easily shown\nthat all non-diagonal terms go to zero very rapidly. [A much larger\npresentation of the theoretical ground on which this paper is based appeared in\nthe e-print quant-ph/9706059, and in the preprint IC/98/74, ICTP; Trieste,\n1998].",
"arxiv_id": "quant-ph/0206117",
"authors": [
"Erasmo Recami",
"Ruy H. A. Farias"
],
"categories": [
"quant-ph"
],
"doi": "10.1393/ncb/i2009-10799-1",
"journal_ref": "Nuovo Cimento B147 (2009) 765-776",
"title": "A simple quantum equation for Decoherence and dissipation (through interaction with the environment)",
"url": "https://arxiv.org/abs/quant-ph/0206117"
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