Abstract
ABSTRACTHere we obtain the explicit difference in the propagator between thermostatted ring-polymer molecular dynamics (TRPMD) and Matsubara dynamics, a recently derived form of linearisation which conserves the quantum Boltzmann distribution. Examination of this approximation leads to the new results that the TRPMD force on the centroid is identical to the Matsubara force on the centroid, and that (in a harmonic potential) the friction matrix can be chosen to produce either the correct oscillation frequency of the higher ring-polymer normal modes or the correct maximum in their position spectrum. This is illustrated with the position-squared autocorrelation function where TRPMD improves upon other similar methods. However, no physical choice of friction resolves qualitatively incorrect fluctuation dynamics at barriers. These results are broadly consistent with previous numerical studies and advise the use of TRPMD for spectra.
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