We present a Monte Carlo technique for sampling from the canonical distribution in molecular dynamics. The method is built upon the Nosé-Hoover constant temperature formulation and the generalized hybrid Monte Carlo method. In contrast to standard hybrid Monte Carlo methods only the thermostat degree of freedom is stochastically resampled during a Monte Carlo step.
@article{M2AN_2009__43_4_743_0,
author = {Leimkuhler, Benedict and Reich, Sebastian},
title = {A Metropolis adjusted Nos\'e-Hoover thermostat},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {43},
year = {2009},
pages = {743-755},
doi = {10.1051/m2an/2009023},
mrnumber = {2542875},
zbl = {1171.82317},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2009__43_4_743_0}
}
Leimkuhler, Benedict; Reich, Sebastian. A Metropolis adjusted Nosé-Hoover thermostat. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 43 (2009) pp. 743-755. doi : 10.1051/m2an/2009023. http://gdmltest.u-ga.fr/item/M2AN_2009__43_4_743_0/
[1] and , GSHMC: An efficient method for molecular simulations. J. Comput. Phys. 227 (2008) 4934-4954. | MR 2414842 | Zbl 1148.82316
[2] , and , Generalized hybrid Monte Carlo methods with and without momentum flip. J. Comput. Phys. 227 (2008) 4934-4954. | MR 2414842 | Zbl 1148.82316
[3] and , Computer Simulation of Liquids. Clarendon Press, Oxford (1987) | Zbl 0703.68099
[4] , and , The Nosé-Poincaré method for constant temperature molecular dynamics. J. Comput. Phys. 151 (1999) 114-134. | MR 1701573 | Zbl 0933.81058
[5] , and , Canonical sampling through velocity rescaling. J. Chem. Phys. 126 (2007) 014101.
[6] , , and , Hybrid Monte-Carlo. Phys. Lett. B 195 (1987) 216-222.
[7] and , Understanding Molecular Simulation. Academic Press, New York (1996). | Zbl 0889.65132
[8] , Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A 31 (1985) 1695-1697.
[9] , A generalized guided Monte-Carlo algorithm. Phys. Lett. B 268 (1991) 247-252.
[10] and , Shadow Hybrid Monte Carlo: An efficient propagator in phase space of macromolecules. J. Comput. Phys. 200 (2004) 581-604. | Zbl 1115.65383
[11] and , Cost of the generalized hybrid Monte Carlo algorithm for free field theory. Nucl. Phys. B 607 (2001) 456-510. | MR 1850796 | Zbl 0969.81639
[12] , Pressure and temperature control in molecular dynamics simulations: a unitary approach in discrete time. Modelling Simul. Mater. Sci. Eng. 6 (1998) 405-421.
[13] , and , Non-ergodicity of the Nose-Hoover thermostatted harmonic oscillator. Arch. Ration. Mech. Anal. 184 (2007) 449-463. | MR 2299758 | Zbl 1122.82002
[14] and , A Hamiltonian formulation for recursive multiple thermostats in a common timescale. SIAM J. Appl. Dyn. Syst. 4 (2005) 187-216. | MR 2136523 | Zbl 1075.92057
[15] , and , A gentle ergodic thermostat for molecular dynamics. J. Stat. Phys. (2009), doi: 10.1007/s10955-009-9734-0. | MR 2505736 | Zbl pre05586412
[16] , Monte Carlo Strategies in Scientific Computing. Springer-Verlag, New York (2001). | MR 1842342 | Zbl 0991.65001
[17] , and , Nose-Hoover chains: The canonical ensemble via continuous dynamics. J. Chem. Phys. 97 (1992) 2635-2643.
[18] , A unified formulation of the constant temperature molecular-dynamics methods. J. Chem. Phys. 81 (1984) 511-519.
[19] , Stochastic Differential Equations. 5th Edition, Springer-Verlag, Berlin-Heidelberg (2000). | Zbl 0567.60055
[20] and , Molecular dynamics of liquid alkanes. Faraday Discussions 66 (1978) 95-107.
[21] , and , Thermostats for “slow'' configurational modes. J. Stat. Phys. 128 (2007) 1321-1336. | MR 2352012 | Zbl 1128.82006