Monte Carlo methods for accelerating barrier crossing: Anti-force-bias and variable step algorithms

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Abstract
For computer simulations of systems in which particles must cross large potential energy barriers, slow convergence is a problem. Basically there are two very disparate time scales: one characterizing motion in the potential wells and one characterizing the rare jumps from one stable well to another. Multiple time scale problems like this sorely test computer resources, and stand in the way of progress on simulations of chain folding, glass transitions, nucleation phenomena, activated barrier crossing, and quantum tunneling processes. Here several new methods are developed and tested on classical and quantum barrier crossings in double well problems. These new methods, called the anti-force-bias and variable step methods, lead to much faster convergence than standard methods. Convergence is tested by studying the deviation in the mean of the cumulative spatial distribution function from the exact distribution function.