Hybrid Monte-Carlo method

The basic scheme of this algorithm is similar to cell-to-cell mapping techniques [14] but differs substantially In one important aspect If applied to larger problems, a direct cell-to-cell approach quickly leads to tremendous computational effort. Only a proper exploitation of the multi-level structure of the subdivision algorithm (also for the eigenvalue problem) may allow for application to molecules of real chemical interest. But even this more sophisticated approach suffers from combinatorial explosion already for moderate size molecules. In a next stage of development [19] this restriction will be circumvented using certain hybrid Monte-Carlo methods. 

Ch. Schiitte, A. Fischer, W. Huisinga, P. Deuflhard. A Hybrid Monte-Carlo Method for Essential Molecular Dynamics. Preprint, Preprint SC 98-04, Konrad Zuse Zentrum, Berlin (1998)... 

B. Mehlig, D. W. Heermann, and B. M. Forrest. Hybrid Monte Carlo method for condensed-matter systems. Phys. Rev. B, 45 679-685, 1992. 

Mackenzie, P.B. An improved hybrid Monte Carlo method. Phys. Lett. B 1989, 226, 369-71. 

Akhmatskaya, E., Bou-Rabee, N., Reich, S. A comparison of generalized hybrid Monte Carlo methods with and without momentum flip. J. Comput. Phys. 2009, 228, 2256-65. 

The hybrid Monte Carlo method of Allancombined Monte Carlo and molecular dynamics steps within the same simulation. Allan et alP have discussed... 

In summary, a promising new method, REPSWA, has been compared and contrasted to existing techniques. Due to its mathematical structure, REPSWA scales linear with system size and has been shown to perform well in model problems. It can easily be combined with parallel tempering and Hybrid Monte Carlo methods to form interesting and exciting novel sampling schemes. These will be described in future work. 

Clark, M. M., Raff, L. M., and Scott, H. L., Hybrid Monte Carlo method for off-lattice simulation of processes involving steps with widely varying rates. Comput Phys 10,584-590 (1996b). 

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