Accelerated Sampling of Boltzmann distributions

Abstract

The sampling of Boltzmann distributions by stochastic Markov processes, can be strongly limited by the crossing time of high (free) energy barriers. As a result, the system may stay trapped in metastable states, and the relaxation time to the equilibrium Boltzmann distribution may be very large compared to the available computational time. In this paper, we show how, by a simple modification of the Hamiltonian, one can dramatically decrease the relaxation time of the system, while retaining the same equilibrium distribution. The method is illustrated on the case of the one-dimensional double-well potential.