Nonlinear optical Galton board: Thermalization and continuous limit

Di Molfetta Giuseppe (1) , Fabrice Debbasch , Marc Brachet

1 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)

The nonlinear optical Galton board (NLOGB), a quantum walk like (but nonlinear) discrete time quantum automaton, is shown to admit a complex evolution leading to long time thermalized states. The continuous limit of the Galton board is derived and shown to be a nonlinear Dirac equation (NLDE). The (Galerkin-truncated) NLDE evolution is shown to thermalize toward states qualitatively similar to those of the NLOGB. The NLDE conserved quantities are derived and used to construct a stochastic differential equation converging to grand canonical distributions that are shown to reproduce the (microcanonical) NLDE thermalized statistics. Both the NLOGB and the Galerkin-truncated NLDE are thus demonstrated to exhibit spontaneous thermalization

Domaines: Physique Quantique [quant-ph]

Di Molfetta Giuseppe, Fabrice Debbasch, Marc Brachet. Nonlinear optical Galton board: Thermalization and continuous limit. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2015, 92 (4), pp.042923. ⟨10.1103/PhysRevE.92.042923⟩. ⟨hal-03594751⟩