The purpose of the present article is to compare different phase-space
sampling methods,
such as purely stochastic methods (Rejection method, Metropolized
independence sampler, Importance Sampling),
stochastically perturbed Molecular Dynamics methods
(Hybrid Monte Carlo, Langevin Dynamics, Biased Random Walk), and purely
deterministic methods (Nosé-Hoover chains, Nosé-Poincaré and Recursive
Multiple Thermostats (RMT) methods). After recalling
some theoretical convergence properties for
the...
We propose a derivation of a nonequilibrium Langevin dynamics for a large particle immersed in a background flow field. A single large particle is placed in an ideal gas heat bath composed of point particles that are distributed consistently with the background flow field and that interact with the large particle through elastic collisions. In the limit of small bath atom mass, the large particle dynamics converges in law to a stochastic dynamics. This derivation follows the ideas of [P. Calderoni,...
The Hartree-Fock exchange operator is an integral operator arising in the Hartree-Fock model as well as in some instances of the density functional theory. In a number of applications, it is convenient to approximate this integral operator by a multiplication operator, i.e. by a local potential. This article presents a detailed analysis of the mathematical properties of various local approximations to the nonlocal Hartree-Fock exchange operator including the Slater potential, the optimized effective...
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