## Introduction

Quantum interference and coherence are phenomena that set the dynamics of molecular scale systems in distinct contrast with the behavior of the macroscopic classical world.1 In chemical physics applications, the creation, evolution, and destruction of quantum coherence plays a central role in a range of physical processes, such as the harvesting and transport of electronic energy in photobiological systems,2–8 the design and interpretation of nonlinear spectroscopies,9 the coherent control of molecular processes,10–12 the manipulation and storage of quantum information,13, 14 and many others.15–17

Quantum coherence exists and is most pronounced in simple few body systems. Decoherence, the irreversible destruction of quantum coherence, is a phenomenon that is associated with complex systems and the resulting interactions between a coherent subsystem and a multidimensional environment or bath. System–bath interactions can never be eliminated completely, and so decoherence is in principle always at work eroding quantum superpositions to their incoherent classical statistical limits. In most formal approaches to dissipative quantum dynamics, the assumption is made that the environment is in thermal equilibrium characterized by a Boltzmann distribution at temperature *T*.18, 19 This is a reasonable approximation in most contexts and greatly simplifies the theoretical analysis.

There are physical situations, however, where nonequilibrium bath effects may be important. For example, light-induced ultrafast coherent electronic processes in chemical or biological systems may occur on time scales that are sufficiently short that initial nonequilibrium states induced in the bath by the excitation may not have a chance to regress to equilibrium. The transient nonequilibrium bath dynamics may undergo nontrivial interplay with the coherent quantum evolution occurring on comparable time scales. On these time scales, the environment has the opportunity to influence the quantum evolution in a manner that is more rich and complex than simply acting to dissipate energy and randomize and destroy quantum phases. Indeed, recent experiments have suggested that the environmental protein dynamics in light harvesting complexes may play an essential role in enhancing quantum energy transport.2–8 In the proposed picture, bath fluctuations aid quantum energy flow by overcoming localization due to energy site inhomogeneities, while at the same time acting to destroy quantum phase coherence.

In this article, we describe recent work on investigating the role of the environment in influencing coherent quantum dynamics. We review numerical methodology developed in our group, based on a semiclassical limit of the quantum Liouville equation, for simulating quantum coherent processes using classical-like molecular dynamics simulation and ensemble averaging, and apply the approach to simulating vibrational dephasing of I_{2} in cryogenic rare gas matrices and the quantum vibrations of OH stretches of HOD in D_{2}O. We then describe a simple analytic and numerical model that highlights novel behavior that can be exhibited by quantum coherent processes in the presence of an environment that is not at thermal equilibrium.