Local scale-invariances in the bosonic contact and pair-contact processes

TL;DR

This paper investigates local scale-invariance in ageing bosonic contact and pair-contact processes, demonstrating that their response and correlation functions align with Schrödinger symmetry predictions, extending understanding of non-equilibrium critical phenomena.

Contribution

It introduces new representations of the Schrödinger group for these processes and confirms local scale-invariance predictions with exact results.

Findings

Two-time response and correlation functions depend only on Schrödinger-invariant parts.

Representation of Schrödinger group derived from free diffusion for contact process.

New Schrödinger group representation related to non-linear Schrödinger equation for pair-contact process.

Abstract

Local scale-invariance for ageing systems without detailed balance is tested through studying the dynamical symmetries of the critical bosonic contact process and the critical bosonic pair-contact process.Their field-theoretical actions can be split into a Schr\"odinger-invariant term and a pure noise term. It is shown that the two-time response and correlation functions are reducible to certain multipoint response functions which depend only on the Schr\"odinger-invariant part of the action. For the bosonic contact process, the representation of the Schr\"odinger group can be derived from the free diffusion equation, whereas for the bosonic pair-contact process, a new representation of the Schr\"odinger group related to a non-linear Schr\"odinger equation with dimensionful couplings is constructed. The resulting predictions of local scale-invariance for the two-time responses and correlators are completely consistent with the exactly-known results in both models.