Related papers: Relaxation to the equilibrium in the hard disk dyn…
The time evolution of the distribution function for a particle-hole excitation in a Fermi system was calculated using the direct numerical solution of a nonlinear diffusion equation in momentum space. A phenomenological expression for…
We obtain exact results for the acceptance ratio and mean squared displacement in Monte Carlo simulations of the simple harmonic oscillator in $D$ dimensions. When the trial displacement is made uniformly in the radius, we demonstrate that…
Using the recently derived Dissipation Theorem and a corollary of the Transient Fluctuation Theorem (TFT), namely the Second Law Inequality, we derive the unique time independent, equilibrium phase space distribution function for an ergodic…
A new Markov Chain Monte Carlo method for simulating the dynamics of molecular systems characterized by hard-core interactions is introduced. In contrast to traditional Kinetic Monte Carlo approaches, where the state of the system is…
Hybrid dynamical systems have proven to be a powerful modeling abstraction, yet fundamental questions regarding the dynamical properties of these systems remain. In this paper, we develop a novel class of relaxations which we use to recover…
On the basis of the dynamical interpretation of Monte Carlo simulations, we discuss the relation of the equilibrium relaxation time, the susceptibility and the statistical error. We introduce a new quantity called {\it the statistical…
This article deals with relaxation approximations of nonlinear systems of hyperbolic balance laws. We introduce a class of relaxation schemes and establish their stability and convergence to the solution of hyperbolic balance laws before…
We study the relaxation of a non-equilibrium carrier distribution under the influence of the electron-electron interaction in the presence of disorder. Based on the Anderson model, our Hamiltonian is composed from a single particle part…
We investigate the positional order of the two-dimensional hard disk model with short-time dynamics and equilibrium simulations. The melting density and the critical exponents z and eta are determined. Our results rule out a phase…
Dynamic relaxation of the XY model and fully frustrated XY model quenched from an initial ordered state to the critical temperature or below is investigated with Monte Carlo methods. Universal power law scaling behaviour is observed. The…
We briefly review some equilibrium and nonequilibrium properties of systems with long-range interactions. Such systems, which are characterized by a potential that weakly decays at large distances, have striking properties at equilibrium,…
A quantum mechanical explanation of the relaxation to equilibrium is shown for macroscopic systems for nonintegrable cases and numerically verified. The macroscopic system is initially in an equilibrium state, subsequently externally…
The control of relaxation-type systems of ordinary differential equations is investigated using the Hamilton-Jacobi-Bellman equation. First, we recast the model as a singularly perturbed dynamics which we embed in a family of controlled…
The magnetic relaxation and hysteresis of a system of single domain particles with dipolar interactions are studied by Monte Carlo simulations. We model the system by a chain of Heisenberg classical spins with randomly oriented easy-axis…
The finite-size scaling method in the equilibrium Monte Carlo(MC) simulations and the finite-time scaling method in the nonequilibrium-relaxation simulations are compromised. MC time data of various physical quantities are scaled by the MC…
We use the technique of information relaxation to develop a duality-driven iterative approach to obtaining and improving confidence interval estimates for the true value of finite-horizon stochastic dynamic programming problems. We show…
It is well known that ergodic theory can be used to formally prove a weak form of relaxation to equilibrium for finite, mixing, Hamiltonian systems. In this Letter we extend this proof to any dynamics that preserves a mixing equilibrium…
We construct a rejection-free Monte Carlo method for the hard-disk system. Rejection-free Monte Carlo methods preserve the time-evolution behavior of the standard Monte Carlo method, and this relationship is confirmed for our method by…
This article is devoted to the long-time dynamics of point-vortex type systems near thermal equilibrium and to the possible emergence of collisional relaxation. More precisely, we consider a tagged particle coupled to a large number of…
We evaluate the relaxation time to equilibrium, and especially show that it is almost independent from the system size for macroscopic isolated quantum systems. It at most polynomially depends on the system size. This estimation holds when…