dorsal/arxiv
View SchemaMultiple-time correlation functions for non-Markovian interaction: Beyond the Quantum Regression Theorem
| Authors | Daniel Alonso, Inés de Vega |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0409098 |
| URL | https://arxiv.org/abs/quant-ph/0409098 |
| DOI | 10.1103/PhysRevLett.94.200403 |
| Journal | Physical Review Letters 94, 200403 (2005) |
Abstract
Multiple time correlation functions are found in the dynamical description of different phenomena. They encode and describe the fluctuations of the dynamical variables of a system. In this paper we formulate a theory of non-Markovian multiple-time correlation functions (MTCF) for a wide class of systems. We derive the dynamical equation of the {\it reduced propagator}, an object that evolve state vectors of the system conditioned to the dynamics of its environment, which is not necessarily at the vacuum state at the initial time. Such reduced propagator is the essential piece to obtain multiple-time correlation functions. An average over the different environmental histories of the reduced propagator permits us to obtain the evolution equations of the multiple-time correlation functions. We also study the evolution of MTCF within the weak coupling limit and it is shown that the multiple-time correlation function of some observables satisfy the Quantum Regression Theorem (QRT), whereas other correlations do not. We set the conditions under which the correlations satisfy the QRT. We illustrate the theory in two different cases; first, solving an exact model for which the MTCF are explicitly given, and second, presenting the results of a numerical integration for a system coupled with a dissipative environment through a non-diagonal interaction.
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"abstract": "Multiple time correlation functions are found in the dynamical description of\ndifferent phenomena. They encode and describe the fluctuations of the dynamical\nvariables of a system. In this paper we formulate a theory of non-Markovian\nmultiple-time correlation functions (MTCF) for a wide class of systems. We\nderive the dynamical equation of the {\\it reduced propagator}, an object that\nevolve state vectors of the system conditioned to the dynamics of its\nenvironment, which is not necessarily at the vacuum state at the initial time.\nSuch reduced propagator is the essential piece to obtain multiple-time\ncorrelation functions. An average over the different environmental histories of\nthe reduced propagator permits us to obtain the evolution equations of the\nmultiple-time correlation functions. We also study the evolution of MTCF within\nthe weak coupling limit and it is shown that the multiple-time correlation\nfunction of some observables satisfy the Quantum Regression Theorem (QRT),\nwhereas other correlations do not. We set the conditions under which the\ncorrelations satisfy the QRT. We illustrate the theory in two different cases;\nfirst, solving an exact model for which the MTCF are explicitly given, and\nsecond, presenting the results of a numerical integration for a system coupled\nwith a dissipative environment through a non-diagonal interaction.",
"arxiv_id": "quant-ph/0409098",
"authors": [
"Daniel Alonso",
"In\u00e9s de Vega"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevLett.94.200403",
"journal_ref": "Physical Review Letters 94, 200403 (2005)",
"title": "Multiple-time correlation functions for non-Markovian interaction: Beyond the Quantum Regression Theorem",
"url": "https://arxiv.org/abs/quant-ph/0409098"
},
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