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

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 rôle 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 Schrödinger algebra appropriate to non-equilibrium dynamics in that the anisotropic ballistic scaling regime can be interpreted in terms of meta-Schrödinger invariance while the regime of isotropic ballistic scaling is meta-conformally invariant.

29 pages, 2 figures

References in corpus (7)

• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• Non-relativistic conformal symmetries and Newton-Cartan structures
• Absence of logarithmic scaling in the ageing behaviour of the 4D spherical model
• Meta-conformal invariance and the boundedness of two-point correlation functions
• Shape dependence of the finite-size scaling limit in a strongly anisotropic $O(\infty )$ model
• Meta-Schrödinger invariance

Cited by in corpus (2)

• Schrödinger symmetry: a historical review
• Physical ageing from generalised time-translation-invariance