Generalized Langevin equation approach for atom/solid-surface scattering: General formulation for classical scattering off harmonic solids

Abstract

A general theoretical framework for introducing many-body or lattice effects into gas/solid scattering is presented. The theory is presently restricted to classical scattering off harmonic lattices but is otherwise completely general. It is nonperturbative and valid for arbitrary lattice temperature. The theory is based on a formulation of lattice dynamics suggested by and related to the Kubo–Mori theory of generalized Brownian motion. This formulation leads to a generalized Langevin equation (GLE) in which only the coordinates of the gas atom and the n∼1–6 surface atoms directly struck by the gas atom appear explicitly. The remainder of the lattice, which functions as a harmonic heat bath, affects the collision through a friction kernel and a Gaussian random force appearing in the GLE. The GLE can be solved in terms of a tractable number of (n+1) -particle gas–surface trajectories using approximate stochastic techniques. Stochastic solution yields thermally averaged temporal gas particle probability distribution functions (pdf). From the long time limit of these pdf’s all temperature dependent gas–surface cross sections can be found. In the limit of zero friction, the theory gives a convenient method for calculating atom–oscillator thermally averaged cross sections which circumvents laborious Monte Carlo classical trajectory sampling and which can be generalized to treat other gas phase collision problems.

Generalization of the escape rate from a metastable state driven by external cross-correlated noise processes

“…In the traditional theory of activated rate processes within the framework of pure thermal fluctuations the equilibrium Boltzmann distribution is necessary to initially thermalize the reactant state [1,2]. On the other hand, for nonequilibrium open system, a constant input of energy through external fluctuating driving force forbids the system to attain the equilibrium state, hence the system approaches (as in our case) towards the steady state (25), an analogue of equilibrium state, to initially energize the reactant state by the effective temperature like quantity (a complex function ofγ 0 , φ 0 and ψ 0 ) embedded in the distribution function (25).…”

“…In the limit of pure thermal processes, i.e. in absence of external fluctuating driving force, it is easy to recover the equilibrium Boltzmann distribution from (25). The justification for using the distribution (25) is the following.…”

MD/FE Multiscale Modeling of Contact

“…This energy dissipation is based on the generalized Langevin equation (GLE) [73][74][75]. One limitation is that the time history kernel is usually derived for a given lattice structure which restricts their usage to crystalline materials.…”

“…The presented method stands on the generalized Langevin equation (GLE) [73][74][75]. The dynamics of atoms inside the coupling region is described using the GLE which incorporates spatial filters as expressed by the following equations:…”

The Development of Models to Optimize Selection of Nuclear Fuels through Atomic-Level Simulation

“…The minimum volume of active and thermostat region must be determined to achieve the maximum efficiency without disturbing the evolution of the cascade. The Langevin thermostat is a stochastic approach to control the system temperature by the use of random forces and damping 46,47 : Here T D is the Debye temperature, k B is the Boltzmann constant, h is the Planck constant, σ 2 is the variance of the random force R(t), m is the mass, Δt is the time step size. Langevin thermostat is known to correctly sample the canonical ensemble and works well for the radiation damage simulation 48 .…”