Mean-field Matsubara dynamics: analysis of path-integral curvature effects in rovibrational spectra
Althorpe, Stuart C
Journal of Chemical Physics
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Althorpe, S. C., & Trenins, G. (2018). Mean-field Matsubara dynamics: analysis of path-integral curvature effects in rovibrational spectra. Journal of Chemical Physics, 149 (014102) https://doi.org/10.1063/1.5038616
It was shown recently that smooth and continuous ‘Matsubara’ phase-space loops follow a quantum-Boltzmann-conserving classical dynamics when decoupled from non-smooth distributions, which was suggested as the reason that many dynamical observables appear to involve a mixture of classical dynamics and quantum Boltz- mann statistics. Here we derive a mean-field version of this ‘Matsubara dynamics’ which sufficiently mitigates its serious phase problem to permit numerical tests on a two-dimensional ‘champagne-bottle’ model of a rotating OH bond. The Matsubara- dynamics rovibrational spectra are found to converge towards close agreement with the exact quantum results at all temperatures tested (200–800 K), the only significant discrepancies being a temperature-independent 22 cm−1 blue-shift in the position of the vibrational peak, and a slight broadening in its lineshape. These results are compared with centroid molecular dynamics (CMD) to assess the importance of non- centroid fluctuations. Above 250 K, only the lowest-frequency non-centroid modes are needed to correct small CMD red-shifts in the vibrational peak; below 250 K, more non-centroid modes are needed to correct large CMD red-shifts and broaden- ing. The transition between these ‘shallow curvature’ and ‘deep curvature’ regimes happens when imaginary-time Feynman paths become able to lower their actions by cutting through the curved potential surface, giving rise to artificial instantons in CMD.
G.T. acknowledges a University of Cambridge Vice-Chancellor’s award and support from St. Catharine’s College, Cambridge. S.C.A. acknowledges funding from the UK Science and Engineering Research Council.
External DOI: https://doi.org/10.1063/1.5038616
This record's URL: https://www.repository.cam.ac.uk/handle/1810/283468