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We show that the classical Rosenbluth method for sampling self-avoiding walks can be extended to a general algorithm for sampling many families of objects, including self-avoiding polygons. The implementation relies on an elementary move which is a generalisation of kinetic growth; rather than only appending edges to the endpoint, edges may be inserted at any vertex providing the resulting objects still lie within the same family. We implement this method using pruning and enrichment to sample self-avoiding walks and polygons. The algorithm can be further extended by mixing it with length-preserving moves, such pivots and crank-shaft moves.
We consider the out-of-equilibrium dynamics of an interacting integrable system in the presence of an external dephasing noise. In the limit of large spatial correlation of the noise, we develop an exact description of the dynamics of the system base
We present a short overview of the recent results in the theory of diffusion and wave equations with generalised derivative operators. We give generic examples of such generalised diffusion and wave equations, which include time-fractional, distribut
We find the complete phase diagram of a generalised XY model that includes half-vortices. The model possesses superfluid, pair-superfluid and disordered phases, separated by Kosterlitz-Thouless (KT) transitions for both the half-vortices and ordinary
A generalised phase-space kinetic Boltzmann equation for highly non-equilibrium charged particle transport via localised and delocalised states is used to develop continuity, momentum and energy balance equations, accounting explicitly for scattering
We review the recent advances on exact results for dynamical correlation functions at large scales and related transport coefficients in interacting integrable models. We discuss Drude weights, conductivity and diffusion constants, as well as linear