From ABC to KPZ

2023/04/05 by Giuseppe Cannizzaro, Patrícia Gonçalves, Cannizzaro, Giuseppe +5 · 2 citations
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Markov Chains and Monte Carlo Methods #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2304.02344

Abstract

We study the equilibrium fluctuations of an interacting particle system evolving on the discrete ring with N∈\mathbb N points, denoted by \mathbb T_N, and with three species of particles that we name A,B and C, but such that at each site there is only one particle. We prove that proper choices of density fluctuation fields (that match those from nonlinear fluctuating hydrodynamics theory) associated to the (two) conserved quantities converge, in the limit N→∞, to a system of stochastic partial differential equations, that can either be the Ornstein-Uhlenbeck equation or the Stochastic Burgers equation. To understand the cross interaction between the two conserved quantities, we derive a general version of the Riemann-Lebesgue lemma which is of independent interest.

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• Derivation of stochastic Burgers on the line with a Dirichlet boundary condition at the origin
• Nonlinear fluctuations for a chain of weakly anharmonic oscillators with stochastic perturbation

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