Dynamical phase transitions in annihilating random walks with pair deposition

Exact results are presented for conditioned dynamics in a system of interacting random walks in one dimension that annihilate immediately when two particles meet on the same site and where pairs of particles are deposited randomly on neighbouring sites. For an atypical hopping activity one finds dynamical nonequilibrium phase transitions analogous to the zero-temperature equilibrium phase transitions that appear in the spin-1/2 quantum XY spin chain in a transverse magnetic field. Along the critical line the approach of the particle density to its stationary value is algebraic with an unexpected mean field exponent. The time-dependent local stationary density correlations are universal with dynamical exponent z = 1. Inside the disordered phase spatially oscillating correlations appear below the typical activity.

Automated summary

Exact results are presented for conditioned dynamics in a system of interacting random walks in one dimension. The system involves particles that annihilate immediately when they meet on the same site, and pairs of particles that are randomly deposited on neighboring sites. The study found dynamical nonequilibrium phase transitions similar to the zero-temperature equilibrium phase transitions in a spin-1/2 quantum XY spin chain in a transverse magnetic field. The approach of the particle density to its stationary value along the critical line is algebraic with an unexpected mean field exponent. The time-dependent local stationary density correlations are universal with a dynamical exponent z = 1. Below the typical activity, spatially oscillating correlations appear inside the disordered phase.