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This note provides an introduction to molecular dynamics, the computational implementation of the theory of statistical physics. The discussion is focused on the properties of Langevin dynamics, a degenerate stochastic differential equation…
Understanding the current-induced vibrational dynamics in molecular nanojunctions is critical for gaining insight into the stability of such systems. While it is well known that Joule heating at higher bias voltages plays an important role…
The reaction A+B --> B is studied when the reactants diffuse in phase space, i.e. their dynamics is described by the Langevin equation. The steady-state rate constants are calculated for both the target (static A and mobile B's) and…
We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano- or micro-scale particles where rolling is an approximation for strong static friction. We consider the simplest possible…
We study the effect of temporal correlation in a Langevin equation describing non-adiabatic dynamics at metal surfaces. For a harmonic oscillator the Langevin equation preserves the quantum dynamics exactly and it is demonstrated that…
Dispersion forces between neutral material bodies are due to fluctuations of the polarization of the bodies. For bodies in equilibrium these forces are often referred to as Casimir-Lifshitz forces. For bodies in relative motion, in addition…
In this paper, we consider Langevin processes with mechanical constraints. The latter are a fundamental tool in molecular dynamics simulation for sampling purposes and for the computation of free energy differences. The results of this…
Brownian motion occurs in a variety of fluids, from rare gases to liquids. The Langevin equation, describing friction and agitation forces in statistical balance, is one of the most successful ways to treat the phenomenon. In rare gases, it…
Using the gauge/string duality, we derive a set of Langevin equations describing the dynamics of a relativistic heavy quark moving with constant average speed through the strongly-coupled N=4 SYM plasma at finite temperature. We show that…
The static friction between crystalline surfaces separated by a molecularly thin layer of adsorbed molecules is calculated using molecular dynamics simulations. These molecules naturally lead to a finite static friction that is consistent…
We prove that for a combined system of classical and quantum particles, it is possible to write a dynamics for the classical particles that incorporates in a natural way the Boltzmann equilibrium population for the quantum subsystem. In…
The underdamped, non-linear, generalized Langevin equation is widely used to model coarse-grained dynamics of soft and biological materials. By means of a projection operator formalism, we show under which approximations this equation can…
In the Langevin formalism, the delicate balance maintained between the fluctuations in the system and their corresponding dissipation may be upset by the presence of a secondary, space-dependent stochastic force, particularly in the low…
The contribution of sliding-induced, atomic-scale instabilities to the kinetic friction force is investigated by molecular dynamics. For this purpose, we derive a relationship between the kinetic friction force $F_{\rm k}$ and the…
We study the statistical properties of the variation of the kinetic energy of a spherical Brownian particle that freely moves in an incompressible fluid at constant temperature. Based on the underdamped version of the generalized Langevin…
The dynamics of a classical heavy particle moving in a quantum environment is determined by a Langevin equation which encapsulates the effect of the environment-induced reaction forces on the particle. For an open quantum system these…
Brownian motion of single particles with various masses M and diameters D is studied by molecular dynamics simulations. Besides the momentum auto-correlation function of the Brownian particle the memory function and the fluctuating force…
We propose a new formulation of the fluctuating lattice Boltzmann equation that is consistent with both equilibrium statististical mechanics and fluctuating hydrodynamics. The formalism is based on a generalized lattice-gas model, with each…
We present an in-depth investigation of heavy-ion fusion dynamics using a six-dimensional Langevin framework that enables unrestricted motion of the asymmetry parameter. The stochastic formalism naturally incorporates friction effects and…
Stochastic thermostats based on the Langevin equation, in which a system is coupled to an external heat bath, are popular methods for temperature control in molecular dynamics simulations due to their ergodicity and their ease of…