Nonlinear Fluctuating Hydrodynamics for Anharmonic Chains

Abstract

With focus on anharmonic chains, we develop a nonlinear version of fluctuating hydrodynamics, in which the Euler currents are kept to second order in the deviations from equilibrium and dissipation plus noise are added. The required model-dependent parameters are written in such a way that they can be computed numerically within seconds, once the interaction potential, pressure, and temperature are given. In principle the theory is applicable to any one-dimensional system with local conservation laws. The resulting nonlinear stochastic field theory is handled in the one-loop approximation. Some of the large scale predictions can still be worked out analytically. For more details one has to rely on numerical simulations of the corresponding mode-coupling equations. In this way we arrive at detailed predictions for the equilibrium time correlations of the locally conserved fields of an anharmonic chain.

Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions

“…[8] for details). The function h KPZ is not known in closed form but has to be evaluated numerically [51] while h LW is, by definition, a Lorentzian.…”

“…[5,6]). More recently, a complete description has been put forward within the nonlinear fluctuating hydrodynamics (NFH) approach, proposed independently by van Beijeren [7] and Spohn [8,9]. These authors have shown that the statistical properties of 1D nonlinear hydrodynamics with three conservation laws (e.g., total energy, momentum, and number of particles) are essentially described by the fluctuating Burgers equation for the field (x,t) with white noise Z,…”

Fluctuating Hydrodynamics Approach to Equilibrium Time Correlations for Anharmonic Chains

“…A proof, which in essence uses only the conservation laws and space-time stationarity of the correlations, is given in [29], see also see [30,31]. Microscopic properties enter only minimally.…”

“…The G-couplings are listed in [29] and as a function of P, β expressed in cumulants up to third order in r 0 , V 0 . The algebra is somewhat messy.…”

Solitons as candidates for energy carriers in Fermi-Pasta-Ulam lattices

“…When nonlinear effects take place, the anomalous energy transport in 1D momentum-conserving lattices is mainly attributed to the Lévy walk of energy carriers on the microscopic level [31][32][33][34][35][36][37][38][39]. On the mesoscopic level, the theory of nonlinear fluctuating hydrodynamics (NFH) is a powerful tool to study the anomalous energy transport in 1D momentum-conserving lattices [40][41][42][43][44]. However, energy carriers in nonlinear lattices have not been identified explicitly so far.…”