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

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 Schrödinger-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 Schrödinger-invariant part of the action. For the bosonic contact process, the representation of the Schrödinger group can be derived from the free diffusion equation, whereas for the bosonic pair-contact process, a new representation of the Schrödinger group related to a non-linear Schrödinger 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.

Slow, bursty dynamics as a consequence of quenched network topologies

“…However, as the GSW model example shows, there are networks that possess smaller topological dimensions, where x < 2. Furthermore, there are other models [40], such as the bosonic contact process or the bosonic pair contact process, where the autocorrelation decays slower (θ = D/2 for these unrestricted CPs [43]), thus x could also be smaller in networks.…”

Ageing, dynamical scaling and its extensions in many-particle systems without detailed balance

“…First, for the computation of the response function, we add the term dR du φ(u, R)h(u, R) to the action. As usual the response function is [9] R(t, s; r, r…”

“…The noiseless three-point response needed for C 1 can be found from its covariance under the ageing algebra [9] …”

Classification of phase transitions in reaction-diffusion models

“…Recently other possible universality classes have been studied 1,27,28,29,30,31,32,33,34,35,36,37,38,39,40 . Among them is a pair contact process with diffusion (PCPD), the critical behavior of which has not yet been described analytically 8,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56 .…”