Coupled Kardar-Parisi-Zhang Equations in One Dimension
arXiv:1306.5643 · doi:10.1007/s10955-013-0842-5
Abstract
Over the past years our understanding of the scaling properties of the solutions to the one-dimensional KPZ equation has advanced considerably, both theoretically and experimentally. In our contribution we export these insights to the case of coupled KPZ equations in one dimension. We establish equivalence with nonlinear fluctuating hydrodynamics for multi-component driven stochastic lattice gases. To check the predictions of the theory, we perform Monte Carlo simulations of the two-component AHR model. Its steady state is computed using the matrix product ansatz. Thereby all coefficients appearing in the coupled KPZ equations are deduced from the microscopic model. Time correlations in the steady state are simulated and we confirm not only the scaling exponent, but also the scaling function and the non-universal coefficients.
32 pages, 4 figures; Minor correction in the formula for the density
References in corpus (5)
- Heat Transport in low-dimensional systems
- Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
- Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
- Statistics of circular interface fluctuations in an off-lattice Eden model
- Spectrum in multi-species asymmetric simple exclusion process on a ring
Cited by in corpus (26)
- Nonlinear fluctuating hydrodynamics for anharmonic chains
- Dynamic Correlators of Fermi-Pasta-Ulam Chains and Nonlinear Fluctuating Hydrodynamics
- Nonlinear Fluctuating Hydrodynamics in One Dimension: the Case of Two Conserved Fields
- Heavy Operators and Hydrodynamic Tails
- Equilibrium time-correlation functions for one-dimensional hard-point systems
- Breakdown of Diffusion on the Edge
- Exact confirmation of 1D nonlinear fluctuating hydrodynamics for a two-species exclusion process
- Universality classes in two-component driven diffusive systems
- Searching for the Tracy-Widom distribution in nonequilibrium processes
- Non-KPZ modes in two-species driven diffusive systems
- Large compact clusters and fast dynamics in coupled nonequilibrium systems
- Exact scaling solution of the mode coupling equations for non-linear fluctuating hydrodynamics in one dimension
- The 1+1 dimensional Kardar-Parisi-Zhang equation: more surprises
- Marching on a rugged landscape: Universality in disordered asymmetric exclusion processes
- Theoretical approaches to the steady-state statistical physics of interacting dissipative units
- Shocks, rarefaction waves, and current fluctuations for anharmonic chains
- Dynamics of coupled modes for sliding particles on a fluctuating landscape
- Hydrodynamic behavior of the 2-TASEP
- Limiting current distribution for a two species asymmetric exclusion process
- KPZ fluctuations in finite volume
- KPZ modes in -dimensional directed polymers
- Out-of-time-ordered correlator in the one-dimensional Kuramoto-Sivashinsky and Kardar-Parisi-Zhang equations
- Miscible-Immiscible Transition and Nonequilibrium Scaling in Two-Component Driven Open Condensate Wires
- Effect of relative timescale on a system of particles sliding on a fluctuating energy landscape: Exact derivation of product measure condition
- Universal spatio-temporal scaling of distortions in a drifting lattice
- Kardar-Parisi-Zhang universality in two-component driven diffusive models: Symmetry and renormalization group perspectives