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On thermalization in classical scalar field theory

Gert Aarts Orcid Logo, Gian Franco Bonini, Christof Wetterich

Nuclear Physics B, Volume: "B587", Issue: 1-3, Pages: 403 - 418

Swansea University Author: Gert Aarts Orcid Logo

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Abstract

Thermalization of classical fields is investigated in a \phi^4 scalar field theory in 1+1 dimensions, discretized on a lattice. We numerically integrate the classical equations of motion using initial conditions sampled from various nonequilibrium probability distributions. Time-dependent expectatio...

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Published in: Nuclear Physics B
ISSN: 05503213
Published: 2000
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URI: https://cronfa.swan.ac.uk/Record/cronfa22617
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Abstract: Thermalization of classical fields is investigated in a \phi^4 scalar field theory in 1+1 dimensions, discretized on a lattice. We numerically integrate the classical equations of motion using initial conditions sampled from various nonequilibrium probability distributions. Time-dependent expectation values of observables constructed from the canonical momentum are compared with thermal ones. It is found that a closed system, evolving from one initial condition, thermalizes to high precision in the thermodynamic limit, in a time-averaged sense. For ensembles consisting of many members with the same energy, we find that expectation values become stationary - and equal to the thermal values - in the limit of infinitely many members. Initial ensembles with a nonzero (noncanonical) spread in the energy density or other conserved quantities evolve to noncanonical stationary ensembles. In the case of a narrow spread, asymptotic values of primary observables are only mildly affected. In contrast, fluctuations and connected correlation functions will differ substantially from the canonical values. This raises doubts on the use of a straightforward expansion in terms of 1PI-vertex functions to study thermalization.
Item Description: @articleAarts:2000mg, author = "Aarts, Gert and Bonini, Gian Franco and Wetterich, Christof", title = "On Thermalization in classical scalar field theory", journal = "Nucl.Phys.", volume = "B587", pages = "403-418", doi = "10.1016/S0550-3213(00)00447-8", year = "2000", eprint = "hep-ph/0003262", archivePrefix = "arXiv", primaryClass = "hep-ph", reportNumber = "HD-THEP-00-20", SLACcitation = "%%CITATION = HEP-PH/0003262;%%",
College: College of Science
Issue: 1-3
Start Page: 403
End Page: 418