Two-time distribution functions in the Gaussian model of randomly forced Burgers turbulence

Abstract

The problem of randomly forced Burgers turbulence ("Burgulence") is considered in terms of the toy Gaussian Larkin model of directed polymers. In terms of the replica technique the explicit expressions for the two-time four-point free energy distribution function is obtained which makes possible to derive the exact result for the two-time velocity distribution function in the corresponding Burgulence problem.

10 pages, 2 figures

References in corpus (5)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Burgers Turbulence
• An exact solution for the KPZ equation with flat initial conditions
• The One-dimensional KPZ Equation and the Airy Process
• $N$-point free energy distribution function in one dimensional random directed polymers