Related papers: Structure preserving noise and dissipation in the …

We study the non-equilibrium dynamics of driven spin lattices in the presence of decoherence caused by either laser phase noise or strong decay. In the first case, we discriminate between correlated and uncorrelated noise and explore their…

We study the role of fluctuations in particle systems modeled by Dean-Kawasaki-type equations, which describe the evolution of particle densities in systems with Brownian motion. By comparing microscopic simulations, stochastic partial…

We continue the work started in Part I of this article, showing how the addition of noise can stabilize an otherwise unstable system. The analysis makes use of nearly optimal Lyapunov functions. In this continuation, we remove the main…

We proposed the modified version of quantum-mechanical theory of continuous measurements for the case of classical open systems. In our approach the influence of measurement on evolution of distribution function of an open system is…

We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the…

Symmetries of the periodic Toda lattice are expresssed in action-angle coordinates and characterized in terms of the periodic and Dirichlet spectrum of the associated Jacobi matrices. Using these symmetries, the phase space of the lattice…

We derive variational integrators for stochastic Hamiltonian systems on Lie groups using a discrete version of the stochastic Hamiltonian phase space principle. The structure-preserving properties of the resulting scheme, such as…

We investigate the fluctuation dynamics of a probe around a deterministic motion induced by interactions with driven particles. The latter constitute the nonequilibrium medium in which the probe is immersed and is modelled as overdamped…

In charged fluids obeying particle-hole symmetry, such as the Dirac fluid in graphene, charge transport is diffusive despite the presence of ballistically propagating sound waves: sound waves "hydrodynamically decouple" from the slower…

In this contribution I discuss a recent proposal of a novel action for lattice gauge theory for finite systems, which accommodates non-periodic spatial boundary conditions. Drawing on the summation-by-parts formulation of finite differences…

In a recent breakthrough Kanzieper showed that it is possible to obtain exact nonperturbative Random Matrix results from the replica limit of the corresponding Painlev\'e equation. In this article we analyze the replica limit of the Toda…

We introduce a physically relevant stochastic representation of the rotating shallow water equations. The derivation relies mainly on a stochastic transport principle and on a decomposition of the fluid flow into a large-scale component and…

In this paper, we have studied the kink and antikink solutions in several neutral scalar models in 1+1 dimension. We follow the standard approach to write down the leading order and the second order force between long distance separated…

The secular evolution of disk galaxies is largely driven by resonances between the orbits of 'particles' (stars or dark matter) and the rotation of non-axisymmetric features (spiral arms or a bar). Such resonances may also explain kinematic…

Coprimeness property was introduced to study the singularity structure of discrete dynamical systems. In this paper we shall extend the coprimeness property and the Laurent property to further investigate discrete equations with complicated…

Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…

We consider a model problem of the scattering of linear acoustic waves in free homogeneous space by an elastic solid. The stress tensor in the solid combines the effect of a linear dependence of strains with the influence of an existing…

We investigate the stochastic dynamics of an active particle moving at a constant speed under the influence of a fluctuating torque. In our model the angular velocity is generated by a constant torque and random fluctuations described as a…

We develop algebro-geometrical approach for the open Toda lattice. For a finite Jacobi matrix we introduce a singular reducible Riemann surface and associated Baker-Akhiezer functions. We provide new explicit solution of inverse spectral…

We examine the linear and nonlinear modes of a one-dimensional nonlinear electrical lattice, where the usual discrete Laplacian is replaced by a fractional discrete Laplacian. This induces a long-range intersite coupling that, at long…