This chapter reviews numerical simulations of quantum field theories based on stochastic quantization and the Langevin equation. The topics discussed include renormalization of finite stepsize algorithms, Fourier acceleration, and the relation of the Langevin equation to hybrid stochastic algorithms and hybrid Monte Carlo. Invited chapter to appear in the special supplement “Stochastic Quantiza...

The escape of the randomly accelerated undamped particle from finite interval under action stochastic resetting is studied. motion such a described by full Langevin equation and characterized position velocity. We compare three protocols, which restarts velocity or (partial resetting) whole (position -- resetting). Using mean first passage time we assess efficiency restarting protocols in facil...

To study relationship between quantum finite automata and probabilistic finite automata, we introduce a notion of probabilistic reversible automata (PRA, or doubly stochastic automata). We find that there is a strong relationship between different possible models of PRA and corresponding models of quantum finite automata. We also propose a classification of reversible finite 1-way automata.