Generalized dephasing relation for fidelity and application as an efficient propagator

Abstract

The dephasing relation (DR), a linearization of semiclassical fidelity, is generalized to include the overlap of "off-diagonal" elements. The accuracy of the formulation is tested in integrable and chaotic systems and its scaling with dimensionality is studied in a Caldeira-Leggett model with many degrees of freedom. It is shown that the DR is often in very good agreement with numerically analytic quantum results and frequently outperforms an alternative semiclassical treatment. Most importantly, since there is no computationally expensive prefactor, and Monte Carlo Metropolis sampling is used to facilitate the calculation, the DR is found to scale remarkably well with increasing dimension. We further demonstrate that a propagator based on the DR can include more quantum coherence and outperform other popular linearized semiclassical methods, such as forward-backward semiclassical dynamics (FBSD) and the linearized semiclassical initial value representation (LSC-IVR).

Efficient on-the-fly ab initio semiclassical method for computing time-resolved nonadiabatic electronic spectra with surface hopping or Ehrenfest dynamics

“…26 Kocia and Heller have extended the method in order to compute the off-diagonal elements of the evolution operator, allowing its use as a general semiclassical propagator. 27 During a revision of our paper, Petit and Subotnik 28 have published a paper in which they compute linear absorption spectra of onedimensional model potentials using a geometric average of correlation functions computed with phase averaging using trajectories propagated on either the ground or excited electronic surface, sometimes obtaining results that are even more accurate than those based on trajectories propagated on the average surface.…”