A Hamiltonian Formulation for Recursive Multiple Thermostats in a Common Timescale

Benedict J. Leimkuhler, Christopher R. Sweet
2005 SIAM Journal on Applied Dynamical Systems  
Molecular dynamics trajectories that sample from a Gibbs distribution can be generated by introducing a modified Hamiltonian with additional degrees of freedom as described by Nosé [S.Nosé, Mol. Phys., 52, 255, 1984] . To achieve the ergodicity required for canonical sampling, a number of techniques have been proposed based on incorporating additional thermostatting variables, such as Nosé-Hoover chains and more recent fully Hamiltonian generalizations. For Nosé dynamics, it is often stated
more » ... the system is driven to equilibrium through a resonant interaction between the self-oscillation frequency of the thermostat variable and a natural frequency of the underlying system. In this article, we clarify this perspective, using harmonic models, and exhibit practical deficiencies of the standard Nosé-chain approach. As a consequence of our analysis, we propose a new powerful "recursive thermostatting" procedure which obtains canonical sampling without the stability problems encountered with Nosé-Hoover and Nosé-Poincaré chains.
doi:10.1137/040606090 fatcat:yinjl7tvsrfldfwdaev4ybe72i