Exact time-dependent solutions of interacting systemsKlobas, Katja (Avtor) Prosen, Tomaž (Mentor) statistical physicsnonequilibrium statistical mechanicssolvable lattice modelscellular automatasolitonsexact resultsmatrix product statestransportIn the thesis we study exact solutions to simple interacting non-equilibrium problems. We propose two lattice models in discrete time, a model of hard-core interacting charged particles and the Rule 54 reversible cellular automata (RCA54). Both systems describe dynamics of particles (solitons) that move with fixed velocities and undergo pairwise scattering. The first problem we study are the transport properties of the model of charged particles. We start by considering the linear response regime. We show that the computation of the relevant correlation functions can be restricted to a subspace of extensive observables, in which the time evolution is simple. This enables us to obtain exact expressions of linear transport coefficients, such as the diffusion constant and Drude weight. A similar approach is applied to the evaluation of the charge profile at large times after starting from a piecewise homogeneous state, and the spatio-temporal charge-charge correlation function. We proceed by studying the full time-evolution of local observables in RCA54. We find an efficient matrix-product state (MPS) that captures the full time-evolved local density. We use the MPS to express the density profile after a special inhomogeneous quench problem, and get an exact expression of the spatio-temporal correlation function. The results show that the model exhibits ballistic transport with diffusive corrections. In the last chapter we consider space-dynamics of RCA54, i.e. dynamics of the dual model that corresponds to the exchange of roles of space and time. We obtain an MPS that encodes all the multi-time correlation functions of ultra-local observables positioned at the same spatial coordinate. We then proceed to formulate space dynamics in terms of local maps with support that is finite, but bigger than that of the local time-evolution maps. We finish by providing an equivalent circuit representation of the dynamics.20202020-09-19 08:15:02Doktorsko delo/naloga120396VisID: 110950COBISS_ID: 30100483sl