Dynamical cooling driven by self-similar fronts in the 2D nonlinear Schr\"odinger model

TL;DR

This paper investigates the self-similar front-driven dynamical cooling in the 2D nonlinear Schrödinger model, revealing multiple similarity ranges and a process akin to an ultraviolet catastrophe.

Contribution

It introduces a detailed analysis of self-similar fronts and their role in dynamical cooling within the 2D nonlinear Schrödinger framework, combining simulations and theoretical models.

Findings

WKE spectrum shows two distinct similarity ranges: quasi-thermal core and ultraviolet tail.

DAM reveals an additional infrared self-similarity range.

Self-similar fronts drive an effective cooling towards a formal equilibrium at zero temperature.

Abstract

We analyze the dynamics towards partial thermalization and subsequent cooling in the defocusing two-dimensional nonlinear Schr\"odinger model, using direct simulations and insights from the wave-kinetic equations (WKE) and a fourth-order differential approximation model (DAM). We show that the evolving WKE spectrum exhibits two distinct similarity ranges--the quasi-thermal core and the ultraviolet tail--whereas in the DAM, an additional range of infrared self-similarity appears. By stretching the quasi-thermal region, the self-similar fronts drive an effective dynamical cooling process towards the formal but ill-defined equilibrium state at vanishing temperature--analogous to an ultraviolet catastrophe in a system of classical waves.