dorsal/arxiv
View SchemaThe Large Time Behaviour in Quantum Field Theory and Quantum Chaos
| Authors | I. Ya. Aref'eva, I. V. Volovich |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9910109 |
| URL | https://arxiv.org/abs/quant-ph/9910109 |
| Journal | Canadian Math.Soc.Conf.Proc. 29 (2000) 15-27 |
Abstract
An exact general formula for the matrix elements of the evolution operator in quantum theory is established. The formul ("ABC-formula") has the form <U(t)>=exp(At+B+C(t)). The constants A and B and the decreasing function C(t) are computed in perturbation theory. The ABC-formula is valid for a general class of Hamiltonians used in statistical physics and quantum field theory. The formula includes the higher order corrections to the well known Weisskopf-Wigner approximation and to the stochastic (van Hove) limit which are widely used in considerations of problems of radiation, decay, quantum decoherence, derivation of master and kinetic equations etc. The function C(t) admits an interpretation as an analogue of the autocorrelation function describing quantum chaos for the quantum baker's map.
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"abstract": "An exact general formula for the matrix elements of the evolution operator in\nquantum theory is established. The formul (\"ABC-formula\") has the form\n\u003cU(t)\u003e=exp(At+B+C(t)). The constants A and B and the decreasing function C(t)\nare computed in perturbation theory. The ABC-formula is valid for a general\nclass of Hamiltonians used in statistical physics and quantum field theory. The\nformula includes the higher order corrections to the well known\nWeisskopf-Wigner approximation and to the stochastic (van Hove) limit which are\nwidely used in considerations of problems of radiation, decay, quantum\ndecoherence, derivation of master and kinetic equations etc. The function C(t)\nadmits an interpretation as an analogue of the autocorrelation function\ndescribing quantum chaos for the quantum baker\u0027s map.",
"arxiv_id": "quant-ph/9910109",
"authors": [
"I. Ya. Aref\u0027eva",
"I. V. Volovich"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"hep-ph",
"math-ph",
"math.MP"
],
"journal_ref": "Canadian Math.Soc.Conf.Proc. 29 (2000) 15-27",
"title": "The Large Time Behaviour in Quantum Field Theory and Quantum Chaos",
"url": "https://arxiv.org/abs/quant-ph/9910109"
},
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