Related papers: Relaxation Processes in Long-Range Lattices
We investigate the lattice spacing dependence of the equilibration time for a recently proposed multiscale thermalization algorithm for Markov chain Monte Carlo simulations. The algorithm uses a renormalization-group matched coarse lattice…
A hierarchy of timescales is ubiquitous in biological systems, where enzymatic reactions play an important role because they can hasten the relaxation to equilibrium. We introduced a statistical physics model of interacting spins that also…
We report a Monte Carlo investigation of the effect of a lattice of antidots on spin relaxation in twodimensional electron systems. The spin relaxation time is calculated as a function of geometrical parameters describing the antidot…
We present a general method to obtain the microcanonical solution of lattice models with long range interactions. As an example, we apply it to the long range Ising chain, focusing on the role of boundary conditions.
We show how reaction coordinate path lengths affect the relaxation efficiency of a complex system. To this purpose, we consider the metric contributions to the transition rates. These metric contributions preserve informations about the…
We study - experimentally, theoretically, and numerically - nonlinear excitations in lattices of magnets with long-range interactions. We examine breather solutions, which are spatially localized and periodic in time, in a chain with…
We investigate quench dynamics in a one-dimensional spin model, comparing both quantum and classical descriptions. Our primary focus is on the different timescales involved in the evolution of the observables as they approach statistical…
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…
We study the relation between short-time vibrational modes and long-time relaxational dynamics in a kinetically constrained lattice gas with harmonic interactions between neighbouring particles. We find a correlation between the location of…
Lattice model with long-range interaction of power-law type that is connected with difference of non-integer order is suggested. The continuous limit maps the equations of motion of lattice particles into continuum equations with fractional…
Lattice models with long-range interactions of power-law type are suggested as a new type of microscopic model for fractional non-local elasticity. Using the transform operation, we map the lattice equations into continuum equation with…
We report on the computer study of a lattice system that relaxes from a metastable state. Under appropriate nonequilibrium randomness, relaxation occurs by avalanches, i.e., the model evolution is discontinuous and displays many scales in a…
We investigate whether small perturbations can cause relaxation to quantum equilibrium over very long timescales. We consider in particular a two-dimensional harmonic oscillator, which can serve as a model of a field mode on expanding…
Relaxation processes in supercooled liquids are known to exhibit interesting as well as complex behavior. One of the hallmarks of this relaxation process observed in the measured auto correlation function is occurrence of multiple steps of…
The connection between domain relaxations at individual scales and the collective heterogeneous response in non-equilibrium systems is a topic of profound interest in recent times. In a model sys- tem of constantly driven oppositely charged…
The nonextensivity of a classical long-range Hamiltonian system is discussed. The system is the so-called $\alpha$-XY model, a lattice of inertial rotators with an adjustable parameter $\alpha$ controlling the range of the interactions.…
We present a unified theory for the longitudinal dynamic response of a stiff polymer in solution to various external perturbations (mechanical excitations, hydrodynamic flows, electrical fields, temperature quenches ...) that can be…
We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…
An extension of the Kinetic Ising model with nonuniform coupling constants on a one-dimensional lattice with boundaries is investigated, and the relaxation of such a system towards its equilibrium is studied. Using a transfer matrix method,…
Exponential relaxation to equilibrium is a typical property of physical systems, but inhomogeneities are known to distort the exponential relaxation curve, leading to a wide variety of relaxation patterns. Power law relaxation is related to…