Mean-field Matsubara dynamics: Analysis of path-integral curvature effects in rovibrational spectra

Abstract

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 Boltzmann 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 toward 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 line shape. 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 broadening. 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.

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Cited by in corpus (10)

• Path-integral dynamics of water using curvilinear centroids
• Quantum dynamics using path integral coarse-graining
• Semiclassical analysis of the quantum instanton approximation
• Testing the quasicentroid molecular dynamics method on gas-phase ammonia
• Multi-time Formulation of Matsubara Dynamics
• Improved torque estimator for condensed-phase quasicentroid molecular dynamics
• Comparison of Matsubara dynamics with exact quantum dynamics for an oscillator coupled to a dissipative bath
• Non-adiabatic Ring Polymer Molecular Dynamics in the Phase Space of the SU(N) Lie Group
• Semiclassical Dynamics in Wigner Phase Space I : Adiabatic Hybrid Wigner Dynamics
• The Early Years of Quantum Monte Carlo (2): Finite Temperature Simulations