Rareevent properties in a classical stochastic model describing the evolution of random unitary circuits
Abstract
We investigate the statistics of selected rare events in a (1 +1 ) dimensional (classical) stochastic growth model which describes the evolution of (quantum) random unitary circuits. In such classical formulation, particles are created and/or annihilated at each step of the evolution process, according to rules which generally favor a growing cluster size. We apply a largedeviation approach based on biased Monte Carlo simulations, with suitable adaptations, to evaluate (a) the probability of ending up with a single particle at a specified final time t_{f} and (b) the probability of having particles outside the light cone, defined by a "butterfly velocity" v_{B}, at t_{f}. Morphological features of singleparticle final configurations are discussed, in connection with whether the location of such particle is inside or outside the light cone; we find that joint occurrence of both events of types (a) and (b) drives significant changes to such features, signaling a secondorder phase transition.
 Publication:

Physical Review E
 Pub Date:
 September 2021
 DOI:
 10.1103/PhysRevE.104.034122
 arXiv:
 arXiv:2109.00645
 Bibcode:
 2021PhRvE.104c4122D
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 11 pages, 12 figures