Ageing without detailed balance in the bosonic contact and pair-contact processes: exact results

TL;DR

This paper provides exact analytical results on ageing phenomena in bosonic contact and pair-contact processes lacking detailed balance, including scaling functions and exponents, enhancing understanding of non-equilibrium critical dynamics.

Contribution

It derives exact two-time correlation and response functions, and determines ageing exponents and scaling functions for these processes, which were previously not explicitly known.

Findings

Exact two-time correlation and response functions derived.

Ageing exponents and scaling functions explicitly calculated.

Distinct ageing exponents identified for autocorrelation and autoresponse in the pair-contact process.

Abstract

Ageing in systems without detailed balance is studied in the exactly solvable bosonic contact process and the critical bosonic pair-contact process. The two-time correlation function and the two-time response function are explicitly found. In the ageing regime, the dynamical scaling of these is analyzed and exact results for the ageing exponents and the scaling functions are derived. For the critical bosonic pair-contact process the autocorrelation and autoresponse exponents agree but the ageing exponents $a$ and $b$ are shown to be distinct.