Dynamics of a quantum interacting system: Extended global approach beyond the Born-Markov and secular approximation

In various fields from quantum physics to biology, the open quantum dynamics of a system consisting of interacting subsystems emphasizes its fundamental functionality. The local approach, deriving a dissipator in a master equation by ignoring the inter-subsystem interaction, has been widely used to describe the reduced dynamics due to its robustness to keep the positivity of a density operator. However, one critique is that a stationary state obtained by the approach in the limit of weak system-environment coupling is written in the form of the Gibbs state for the partial Hamiltonian by excluding the inter-subsystem interaction from the total one of the relevant system. As an alternative, the global approach, deriving a dissipator with including the inter-subsystem interaction, under the Born--Markov and secular approximations has attracted much attention, and there is debate concerning its violation of positivity in the short-term region and/or limited parameter region for the Bohr frequencies of the subsystems. In this study, we present a formalism that leads to the time-convolutionless (time-local) master equation obtained by extending the global approach beyond the Born-Markov and secular approximations. We apply it to the excitation energy transfer between interacting sites in which only the terminal site weakly interacts with a bosonic environment of finite temperature in a manner beyond the rotating-wave approximation. We find that the formulation (1) gives the short-time behavior while preserving positivity, (2) shows the oscillatory features that the secular approximation would obscure, and (3) leads to a stationary state very near to the Gibbs state for the total Hamiltonian of the relevant system.Comment: 14 pages, 8 figure

Environmental engineering for quantum energy transport

Transport phenomena are ubiquitous throughout the science, engineering and technology disciplines as it concerns energy, mass, charge and information exchange between systems. In particular, energy transport in the nanoscale regime has attracted significant attention within the physical science community due to its potential to explain complex phenomena like the electronic energy transfer in molecular crystals or the Fenna-Matthews-Olson / light harvesting complexes in photosynthetic bacteria with long time coherences. Energy transport in these systems is highly affected by environmental noise but surprisingly not always in a detrimental way. It was recently found that situations exist where noise actually enhances the transport phenomena. Such noise can take many forms, but can be characterised in three basic behaviours: quantum, coloured or nonlocal. All have been shown potential to offer an energy transport enhancement. The focus of this work is on quantum transport caused by stochastic environment with spatio-temporal correlation. We consider a multi-site nearest neighbour interaction model with pure dephasing environmental noise with coloured and nonlocal character and show how an accelerated rate for the energy transfer results especially under anti-correlation. Negative spatial correlations provide another control parameter to help one establish the most efficient transfer of energy and may provide new insights into the working of exciton transport in photosynthetic complexes. Further the usage of spatio-temporal correlated noise may be a beneficial resource for efficient transport in large scale quantum networks.Comment: 11 pages 5 figure