Lagrangian statistical mechanics applied to non-linear stochastic field equations

Sam F. Edwards and Moshe Schwartz

Physica A: Statistical Mechanics and its Applications, 2002, vol. 303, issue 3, 357-386

Abstract: We consider non-linear stochastic field equations such as the KPZ equation for deposition and the noise driven Navier–Stokes equation for hydrodynamics. We focus on the Fourier transform of the time dependent two-point field correlation, Φk(t). We employ a Lagrangian method aimed at obtaining the distribution function of the possible histories of the system in a way that fits naturally with our previous work on the static distribution. Our main result is a non-linear integro-differential equation for Φk(t), which is derived from a Peierls–Boltzmann type transport equation for its Fourier transform in time Φk,ω. That transport equation is a natural extension of the steady state transport equation, we previously derived for Φk(0). We find a new and remarkable result which applies to all the non-linear systems studied here. The long time decay of Φk(t) is described by Φk(t)∼exp(−a|k|tγ), where a is a constant and γ is system dependent.

Keywords: Non-linear stochastic field equations; Correlation function; Ballistic deposition (search for similar items in EconPapers)
Date: 2002
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:303:y:2002:i:3:p:357-386

DOI: 10.1016/S0378-4371(01)00479-4

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