Related papers: Classical Langevin Dynamics for Model Hamiltonians
The expansion of a classical Hamilton formalism consisting in adaptation of it to describe the nonequilibrium systems is offered. Expansion is obtained by construction of formalism on the basis of the dynamics equation of the equilibrium…
The classical work by Zwanzig [J. Stat. Phys. 9 (1973) 215-220] derived Langevin dynamics from a Hamiltonian system of a heavy particle coupled to a heat bath. This work extends Zwanzig's model to a quantum system and formulates a more…
Many living and complex systems exhibit second order emergent dynamics. Limited experimental access to the configurational degrees of freedom results in data that appears to be generated by a non-Markovian process. This poses a challenge in…
Reconstruction of equations of motion from incomplete or noisy data and dimension reduction are two fundamental problems in the study of dynamical systems with many degrees of freedom. For the latter extensive efforts have been made but…
Many complex systems operating far from the equilibrium exhibit stochastic dynamics that can be described by a Langevin equation. Inferring Langevin equations from data can reveal how transient dynamics of such systems give rise to their…
The recently discovered supersymmetric generalizations of Langevin dynamics and Kramers equation can be utilized for the exploration of free energy landscapes of systems whose large time-scale separation hampers the usefulness of standard…
Recent rapid advances in single particle tracking and supercomputing techniques resulted in an unprecedented abundance of diffusion data exhibiting complex behaviours, such the presence of power law tails of the msd and memory functions,…
Previously developed ``stochastic representation of deterministic interactions`` enables exact treatment of an open system without leaving its native phase space (Hilbert space) due to peculiar stochastic extension of the Liouville (von…
We consider a classical model of non-equilibrium statistical mechanics accounting for non-Markovian effects, which is referred to as the Generalized Langevin Equation in the literature. We derive reduced Markovian descriptions obtained…
Given nonstationary data from molecular dynamics simulations, a Markovian Langevin model is constructed that aims to reproduce the time evolution of the underlying process. While at equilibrium the free energy landscape is sampled,…
Hamilton's principle is extended to have compatible initial conditions to the strong form. To use a number of computational and theoretical benefits for dynamical systems, the mixed variational formulation is preferred in the systems other…
For a system at given temperature, with energy known as a function of a set of variables, we obtain the thermal fluctuation of the evolution of the variables by replacing the phase-space with a lattice and invoking the principle of detailed…
The advantages of performing Langevin Dynamics in extended systems are discussed. A simple Langevin Dynamics scheme for producing the canonical ensemble is reviewed, and is then extended to the Hoover ensemble. We show that the resulting…
We present in detail a Langevin formalism for constructing stochastic dynamical equations for active-matter systems coupled to a thermal bath. We apply the formalism to clarify issues of principle regarding the sources and signatures of…
We describe a simple stochastic method, so-called Langevin approach, which enables one to extract evolution equations of stochastic variables from a set of measurements. Our method is parameter-free and it is based on the nonlinear Langevin…
The Mori-Zwanzig formalism is applied to derive an equation for the evolution of linear observables of the overdamped Langevin equation. To illustrate the resulting equation and its use in deriving approximate models, a particular benchmark…
In this paper a one-dimensional model of two infinite gases separated by a movable heavy piston is considered. The non-linear Langevin equation for the motion of the piston is derived from first principles for the case when the…
The problem of effective equations is reviewed and discussed. Starting from the classical Langevin equation, we show how it can be generalized to Hamiltonian systems with non-standard kinetic terms. A numerical method for inferring…
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
The classical Hamilton equations of motion yield a structure sufficiently general to handle an almost arbitrary set of ordinary differential equations. Employing elementary algebraic methods, it is possible within the Hamiltonian structure…