Abstract
We present an approach to investigate the long-time stochastic dynamics of multidimensional classical systems, in contact with a heat bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short- and long-time scales and both molecular dynamics or Monte Carlo (MC) simulations are generally inefficient. Using a field theoretic approach, we perform analytically the average over the short-time stochastic fluctuations. This way, we obtain an effective theory, which generates the same long-time dynamics of the original theory, but has a lower time-resolution power. Such an approach is used to develop an improved version of the MC algorithm, which is particularly suitable to investigate the dynamics of rare conformational transitions. In the specific case of molecular systems at room temperature, we show that elementary integration time steps used to simulate the effective theory can be chosen a factor approximately 100 larger than those used in the original theory. Our results are illustrated and tested on a simple system, characterized by a rugged energy landscape.
Highlights
The investigation of a vast class of physical phenomena requires the understanding of the long-time dynamics of classical systems, in contact with a heat-bath
When the potential energy landscape is rugged, the kinetics displays a decoupling of short- and long-time scales and both molecular dynamics or Monte CarloMCsimulations are generally inefficient
In the specific case of molecular systems at room temperature, we show that elementary integration time steps used to simulate the effective theory can be chosen a factor ϳ100 larger than those used in the original theory
Summary
The investigation of a vast class of physical phenomena requires the understanding of the long-time dynamics of classical systems, in contact with a heat-bath. We are interested in constructing an efficient algorithm to perform numerical simulation long-time dynamics To this goal, we use a field theory approach, based on renormalization groupRGideas and on the notion of effective field theory8͔. The average over the fast thermal oscillations gives rise to new terms in the stochastic path integral, which represent corrections both to the interaction and to the diffusion coefficient Such new terms implicitly take into account of the dynamics of the fast degrees of freedom, which have been integrated out from the system. II, we review the path integral formulation of the Langevin dynamics and we outline the formal connection between stochastic dynamics and evolution of a quantum particle in imaginary time
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