Dynamical symmetries in the non-equilibrium dynamics of the directed spherical model

TL;DR

This paper investigates the non-equilibrium dynamics of the directed spherical model, revealing new ballistic scaling regimes and their symmetries, extending the understanding of aging and correlations in such systems.

Contribution

It introduces exact analysis of two-time correlation and response functions, identifying novel anisotropic ballistic scaling regimes and their associated dynamical symmetries.

Findings

Discovery of anisotropic ballistic scaling regimes

Identification of meta-Schr"odinger and meta-conformal invariance in these regimes

Clarification of the role of initial correlations in scaling behavior

Abstract

The dynamical scaling and ageing in the relaxational dynamics of the quenched directed spherical model is analysed. The exact two-time correlation and response functions display new regimes of ballistic or anisotropic ballistic scaling, at larger distances than probed in the usual regime of diffusive scaling. The r\^ole of long-ranged initial correlations on the existence of these scaling regimes is clarified. Their dynamical symmetries are described in terms of extensions of the Schr\"odinger algebra appropriate to non-equilibrium dynamics in that the anisotropic ballistic scaling regime can be interpreted in terms of meta-Schr\"odinger invariance while the regime of isotropic ballistic scaling is meta-conformally invariant.