Leimkuhler, Benedict J.; Sweet, Christopher R. A Hamiltonian formulation for recursive multiple thermostats in a common timescale. (English) Zbl 1075.92057 SIAM J. Appl. Dyn. Syst. 4, No. 1, 187-216 (2005). Summary: 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 S. Nosé [Mol. Phys. 52, 255 ff (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 that 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. 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. Cited in 7 Documents MSC: 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.) 92E99 Chemistry 81V55 Molecular physics 37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems Keywords:Nosé-Poincaré chains; symplectic integrator; constant temperature molecular dynamics; thermostatting PDFBibTeX XMLCite \textit{B. J. Leimkuhler} and \textit{C. R. Sweet}, SIAM J. Appl. Dyn. Syst. 4, No. 1, 187--216 (2005; Zbl 1075.92057) Full Text: DOI Link