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A Hamiltonian formulation for recursive multiple thermostats in a common timescale. (English) Zbl 1075.92057

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.

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
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