Lagrangian Statistical Mechanics applied to Non-linear Stochastic Field Equations

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dc.creatorEdwards, Sam F.
dc.creatorSchwartz, Moshe
dc.date2000-12-04
dc.date2001-09-27
dc.date.accessioned2026-07-07T02:39:39Z
dc.date.available2026-07-07T02:39:39Z
dc.descriptionWe 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, $Φ_{\bf{k}}(t)$. 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 $Φ_{\bf{k}}(t)$, which is derived from a Peierls-Boltzmann type transport equation for its Fourier transform in time $Φ_{\bf{k}, ω}$. That transport equation is a natural extension of the steady state transport equation, we previously derived for $Φ_{\bf{k}}(0)$. We find a new and remarkable result which applies to all the non-linear systems studied here. The long time decay of $Φ_{\bf{k}}(t)$ is described by $Φ_{\bf{k}}(t) \sim \exp(-a|{\bf k}|t^γ)$, where $a$ is a constant and $γ$ is system dependent.
dc.description67 pages, 2 figures, corrected version
dc.identifierhttps://arxiv.org/abs/cond-mat/0012044
dc.identifierhttp://arxiv.org/abs/cond-mat/0012044
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/17098
dc.subjectStatistical Mechanics
dc.titleLagrangian Statistical Mechanics applied to Non-linear Stochastic Field Equations
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