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We consider the Bethe ansatz solution of integrable models interacting through factorized $S$-matrices based on the central extention of the $\bf{su}(2|2)$ symmetry. The respective $\bf{su}(2|2)$ $R$-matrix is explicitly related to that of…

We study the asymmetric exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system. We further consider the thermodynamic limit, showing…

We prove fluctuation bounds for the particle current in totally asymmetric zero range processes in one dimension with nondecreasing, concave jump rates whose slope decays exponentially. Fluctuations in the characteristic directions have…

A theoretical analysis is given of the equation of motion method, due to Alben et al., to compute the eigenvalue distribution (density of states) of very large matrices. The salient feature of this method is that for matrices of the kind…

Homogeneous mass fragmentation processes describe the evolution of a unit mass that breaks down randomly into pieces as time. Mathematically speaking, they can be thought of as continuous-time analogues of branching random walks with…

We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model…

It is known that the distribution of nonreversible Markov processes breaking the detailed balance condition converges faster to the stationary distribution compared to reversible processes having the same stationary distribution. This is…

Meta-atoms, nano-antennas, plasmonic particles and other small scatterers are commonly modeled in terms of their modes. However these modal solutions are seldom determined explicitly, due to the conceptual and numerical difficulties in…

We consider matrix-valued processes described as solutions to stochastic differential equations of very general form. We study the family of the empirical measure-valued processes constructed from the corresponding eigenvalues. We show that…

We formulate a new integrable asymmetric exclusion process with $N-1=0,1,2,...$ kinds of impurities and with hierarchically ordered dynamics. The model we proposed displays the full spectrum of the simple asymmetric exclusion model plus new…

We study the fragment size distributions after crushing of single and many particles under uniaxial compression inside a cylindrical container by means of numerical simulations. Under the assumption that breaking goes through the bulk of…

We consider a mobile impurity particle injected into a one-dimensional quantum gas. The time evolution of the system strongly depends on whether the mass of the impurity and the masses of the host particles are equal or not. For equal…

For reaction-diffusion processes without exclusion, in which the particles can exist in the same site of a one-dimensional lattice, we study all the integrable models which can be obtained by imposing a boundary condition on the master…

The goal of this article is to study the limit of the empirical distribution induced by a mutation-selection multi-allelic Moran model, whose dynamic is given by a continuous-time irreducible Markov chain. The rate matrix driving the…

We discuss methods for numerically solving the generalized Master equation GME which governs the time-evolution of the reduced density matrix of a mechanically movable mesoscopic device in a dissipative environment. As a specific example,…

Entanglement sharing among sites of one-particle states is considered using the measure of concurrence. These are the simplest in an hierarchy of number-specific states of many qubits and corresponds to ``one-magnon'' states of spins. We…

This paper discusses a numerical method for computing the evolution of large interacting system of quantum particles. The idea of the random batch method is to replace the total interaction of each particle with the $N-1$ other particles by…

We analyze the response of a complex quantum-mechanical system (e. g., a quantum dot) to a time-dependent perturbation. Assuming the dot energy spectrum and the perturbation to be described by the Gaussian Orthogonal Ensemble of random…

Given a random quantum state of multiple distinguishable or indistinguishable particles, we provide an effective method, rooted in symplectic geometry, to compute the joint probability distribution of the eigenvalues of its one-body reduced…

We consider the joint distribution of real and imaginary parts of eigenvalues of random matrices with independent entries with mean zero and unit variance. We prove the convergence of this distribution to the uniform distribution on the…