Related papers: Equilibration problem for the generalized Langevin…
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…
The potential of mean force (PMF) is an effective average potential acting on an open system, renormalized due to the interaction with the surrounding thermal bath. The PMF determines the correction to the equilibrium Gibbs distribution,…
In this research paper, we present an exact matrix form analytical solution of the multi-dimensional generalized Langevin equation with quadratic potentials. Our investigation provides detailed expressions for the two-dimensional…
We study the collective escape dynamics of a chain of coupled, weakly damped nonlinear oscillators from a metastable state over a barrier when driven by a thermal heat bath in combination with a weak, globally acting periodic perturbation.…
We study the Langevin dynamics of a heteropolymer by means of a mode-coupling approximation scheme, giving rise to a set of coupled integro-differential equations relating the response and correlation functions. The analysis shows that…
We present here a conjecture about the equivalence between the noise density of states of a system governed by a generalized Langevin equation and the fluctuation in the energy density of states in a Hamiltonian system. We present evidence…
Starting from a microscopic theory, we derive a master equation for a harmonic oscillator coupled to a bath of non-interacting oscillators. We follow a non-perturbative approach, proposed earlier by us for the free Brownian particle. The…
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…
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…
We propose a system composed of a qubit interacting with a quartic (undriven) nonlinear oscillator (NLO) through a conditional displacement Hamiltonian. We show that even a modest nonlinear perturbation in the NLO potential can enhance and…
We study the relaxational dynamics of flux lines in high-temperature superconductors with random pinning using Langevin dynamics. At high temperatures the dynamics is stationary and the fluctuation dissipation theorem (FDT) holds. At low…
Perceptrons are the building blocks of many theoretical approaches to a wide range of complex systems, ranging from neural networks and deep learning machines, to constraint satisfaction problems, glasses and ecosystems. Despite their…
The process of equilibration of a colliding hard-disks system is studied in the framework of classical mechanic. The method consists of dividing the nonequilibrium system into the interacting subsystems; the evolution one of these…
Dissipation using a finite environment coupled to a single harmonic oscillator have been studied quite extensively. We extend the study by looking at the dynamics of the dissipation when we introduce a second bath of N identical quartic…
It is known that in the regime of superlinear diffusion, characterized by zero integral friction (vanishing integral of the memory function), the generalized Langevin equation may have non-ergodic solutions which do not relax to equilibrium…
We study the equilibration dynamics of closed finite quantum systems and address the question of the time needed for the system to equilibrate. In particular we focus on the scaling of the equilibration time T_{\mathrm{eq}} with the system…
This paper investigates the global dynamics of the discontinuous limit case of an archetypal oscillator with constant excitation that exhibits a single equilibrium. For parameter regions in which this oscillator possesses two or three…
We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…
Usually, the relaxation times of a gas are estimated in the frame of the Boltzmann equation. In this paper, instead, we deal with the relaxation problem in the frame of the dynamical theory of Hamiltonian systems, in which the definition…
Coarse-grained Langevin-type effective field equations are derived for classical systems of particles. These equations include the effects of thermal fluctuation and dissipation which may arise from coupling to an external bath, as in the…