Newtonian versus Langevin dynamics: Example of ϕ4-model with infinite range interactions

V.G. Rostiashvili

Physica A: Statistical Mechanics and its Applications, 1996, vol. 231, issue 4, 575-587

Abstract: The functional integral representation for the generating functional (GF) of the canonically averaged ensemble with an underlying Newtonian dynamics is obtained. It is shown that for this representation the non-linear fluctuation-dissipation theorem (NFDT) has the same form as for the Langevin dynamics case. This GF-representation is used for the investigation of the dynamics of the ϕ4-model with infinite range interactions at T > Tc. It is shown that the kinetic equation for the complete correlation function has the same form as for the Langevin dynamics case, which was considered before. All peculiarities of Newtonian dynamics are absorbed by one-particle (2-point and 4-point) correlator and response functions. The analysis of this equation shows that the 1/N-fluctuations (where N is the number of particles) restore the ergodicity of the system with the characteristicsrate τ−1 ∼ μ2/N, where μ is a coupling constant.

Keywords: Generating functional technique; Functional integral representation; Fluctuation-dissipation theorem; Newtonian dynamics; Langevin dynamics; Models with infinite range interactions (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:231:y:1996:i:4:p:575-587

DOI: 10.1016/0378-4371(96)00096-9

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