Optical Dephasing of Ions and Molecules in Crystals

A hybrid memory kernel approach for condensed phase non-adiabatic dynamics

The spin-boson model is a simplified Hamiltonian often used to study non-adiabatic dynamics in large condensed phase systems, even though it has not been solved in a fully analytic fashion. Herein, we present an exact analytic expression for the dynamics of the spin-boson model in the infinitely slow-bath limit and generalize it to approximate dynamics for faster baths. We achieve the latter by developing a hybrid approach that combines the exact slow-bath result with the popular non-interacting blip approximation (NIBA) method to generate a memory kernel that is formally exact to second-order in the diabatic coupling but also contains higher-order contributions approximated from the second-order term alone. This kernel has the same computational complexity as the NIBA, but is found to yield dramatically superior dynamics in regimes where the NIBA breaks down-such as systems with large diabatic coupling or energy bias. This indicates that this hybrid approach could be used to cheaply incorporate higher-order effects into second-order methods and could potentially be generalized to develop alternate kernel resummation schemes.

Infrared and Raman line shapes for ice Ih. I. Dilute HOD in H(2)O and D(2)O

Vibrational spectroscopy of ice Ih provides information about structure, dynamics, and vibrational coupling in this important substance. Vibrational spectra are simplified for HOD in either H(2)O or D(2)O, as in these instances the OD or OH stretch, respectively, functions as a local chromophore. As a first step in providing a theoretical treatment of the vibrational spectroscopy for the fully coupled system (H(2)O or D(2)O), herein we calculate the infrared and Raman spectra for the isotopically substituted systems. The calculation involves a classical molecular dynamics simulation using a new water model, an initial proton-disordered ice configuration, and ab initio based transition frequency, dipole, and polarizability maps. Our theoretical results are in reasonable agreement with experiment, and from our results we provide molecular and physical interpretations for the spectral features.

Nonequilibrium quantum dynamics in the condensed phase via the generalized quantum master equation

The Nakajima-Zwanzig generalized quantum master equation provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a quantum bath. In this equation, the memory kernel accounts for the influence of the bath on the system's dynamics, and the inhomogeneous term accounts for initial system-bath correlations. In this paper, we propose a new approach for calculating the memory kernel and inhomogeneous term for arbitrary initial state and system-bath coupling. The memory kernel and inhomogeneous term are obtained by numerically solving a single inhomogeneous Volterra equation of the second kind for each. The new approach can accommodate a very wide range of projection operators, and requires projection-free two-time correlation functions as input. An application to the case of a two-state system with diagonal coupling to an arbitrary bath is described in detail. Finally, the utility and self-consistency of the formalism are demonstrated by an explicit calculation on a spin-boson model.