One-Parametric Family of the Double-Scaling Limits in the Hermitian Matrix Model $\Phi^6:$ Onset of Nondissipative Shock Waves

TL;DR

This paper introduces a new family of double-scaling limits in the Hermitian trix model , connecting quantum gravity and shock wave phenomena, with numerical simulations supporting the theoretical framework.

Contribution

It constructs a one-parametric family of double-scaling limits in the trix model , linking quantum gravity with solutions of the Korteweg-de Vries equation.

Findings

The family includes the known Bresin, Marinari, and Parisi limit.

The Gurevich-Pitaevskii solution models the onset of nondissipative shock waves.

Numerical simulations confirm the universality of the solution.

Abstract

We construct a one-parametric family of the double-scaling limits in the hermitian matrix model $\Phi^6$ for 2D quantum gravity. The known limit of Bresin, Marinari and Parisi belongs to this family. The family is represented by the Gurevich-Pitaevskii solution of the Korteveg-de Vries equation which describes the onset of nondissipative shock waves in media with small dispersion. Numerical simulation of the universal Gurevich-Pitaevskii solution is made.