Nonequilibrium statistical physics in discrete space-timeKrajnik, Žiga (Avtor) Prosen, Tomaž (Mentor) classical integrabilitydiscrete space-timeinverse scattering methodsoliton gasspin transportsuperdiffusionfull-counting statisticscharged single-file dynamicsdynamical criticalityanomalous spin dynamicsWe study the equilibrium and non-equilibrium statistical properties of interacting many-body systems, focusing on classical integrable models in one spatial dimensions. While integrability allows one to solve the initial value problem for a nonlinear system, the averaging over ensembles of initial conditions, implicit in a statistical description, is analytically intractable. Even numerical simulations of integrable systems are delicate since direct discretization invariably break integrability. By embedding an integrable system as a compatibility condition of a pair of linear problems, we instead define families of classical integrable system on a discrete space-time lattice, whose limits are Hamiltonian lattice/field-theory integrable models and facilitate their efficient numerical simulations. We solve the initial value problem of a model in discrete space-time by using the inverse scattering transform and formulate its thermodynamics within the soliton gas approximation. By using the defined integrable discretization, we study spin transport in the anisotropic lattice Landau–Lifshitz model. In integrable spin chains with non-abelian symmetry we find spin superdiffusion with the scaling function of the Kardar-Parisi-Zhang universality class. A refined view of dynamics is given by full-counting statistics of conserved quantities. We introduce the class of charged single-file systems and demonstrate their dynamical universality which we study in detail. We detect robust signs of dynamical criticality in the anisotropic lattice Landau–Lifshitz model and find an unexpected connection with charged single-file systems.20232023-08-25 08:15:03Doktorsko delo/naloga148491sl