The accurate treatment, and detailed understanding of coherent quantum dynamics in open systems, for example, the non-equilibrium evolution of a quantum subsystem embedded in complex nano-structured many-body environment, may be crucial for the determining the properties and functioning of natural and artificial nanoscale devices or nano-structured materials. For example, recent experiments [1] have demonstrated that, even at room temperature, conjugated polymer systems exhibit coherent intra-chain energy migration by apparently coupling exciton transfer to a vibrational mode of the polymer [2] whose correlation length is long compared to the spacing between chromophores, thus fluctuations in the energies of the different chromophores are dynamically correlated and these motions can protect the coherent superposition of chromophore states from dephasing. This ubiquitous phenomenon has also been seen in a series of remarkable recent experiments [3,4] that have implicated long-lived coherent quantum exciton dynamics, protected by correlated motions in the environment between chromophores, as apparently being responsible for the extraordinary efficiencies of energy transfer in natural photosynthetic light harvesting complexes[5,6]. The quantum coherence seems to play an important role in the lossless delivery of excitation energy from the harvesting antenna array to the reaction center where energy conversion and storage processes begin. Thus understanding coherent quantum dynamics in open systems, and more importantly being able to accurately model such dynamics in detail may, for example, reveal the design principles that nature employs in assembling arrays of chromophores and enable the construction of biomimetic light harvesting antenna arrays to dramatically improve the efficiency of photovoltaic systems, or utilize novel properties of conducting polymers that arise from their ability to transfer energy coherently over comparatively long distances. Understanding how driving environmental modes to correlate fluctuations around different chromophores and protect their coherent superposition states from dephasing may also be useful for controlling decoherence lifetimes for applications in quantum information theory [5].

Many different approximate methods for treating quantum dynamics in open systems have been developed. The simplest approach, for example uses semiclassical methods that invoke "hopping" of excited state populations among discrete energy levels and neglects coherence altogether [6]. To overcome this limitation, other methods, including multi-chromophore-FRET [7], various versions of Redfield theory [8], and the Lindbland master equation based on alternative versions of perturbation theory and/or projection operator approaches [9,10,11], have been widely used. These treatments, however, all assume weak electronic or environmental coupling and experimental evidence suggests that these assumptions cannot hold for some of the interesting system outlined above. Furthermore, with all these perturbation approaches it is generally very difficult to incorporate the effects of correlations between environmental modes that modulate the coupling between different chromophores. A common assumption with these approaches is thus that each chromophore interacts with its own independent bath. This assumption too is questioned by evidence from experiments on these systems. Other methods based mixed-quantum classical ideas have been developed including:  an Iterative density matrix propagation scheme[12], the mixed quantum-classical Wigner-Liouville approach [13,14], or truncated hierarchical moment expansions [15]. These methods are capable of approximating longtime coherent quantum dynamics in challenging many-body model systems and, due to the quasi-classical treatment of many of the degrees of freedom these calculations are still computationally tractable for large systems. Highly efficient guided basis set expansion methods such as multiple spawning, and optimal coherent state basis set methods also offer ways of, in principle, performing exact quantum dynamics calculations on models of these systems. Path integral methods also have been developed to study these systems [16]. Similarly MCTDH methods can now provide exact quantum dynamics results for a wide range of model problems [17] that exhibit many of the interesting coherence effects outlined above and can be extended to hundreds of appropriate degrees of freedom. Variations on these theories have been developed and extended to describe coherent multidimensional optical spectra [18].