Coherent resonance energy transfer dynamics of super-Ohmic environments experiencing logarithmic perturbations using full polaron transformation-based approach and its performance

Resonance energy transfer between an excited donor and a potential acceptor is a highly researched area in science. Multiple theories have been introduced in the literature to understand and simulate this energy transfer. The formulation of quantum master equation incorporating full polaron transformation approach is one of the approximation methods for simulating dynamics of the coherent resonance energy transfer. Full polaron based quantum master equation is well known for undergoing infrared divergence for Ohmic and sub-Ohmic environments where the spectral density function scales linearly or sub-linearly at low frequencies. Our objective of this paper is to study an environment where logarithmic perturbations can be experienced with a full polaron based quantum master equation and gauge its performance. In doing so, we study how a perturbation in the frequency domain affects the overall quantum coherence of the energy transfer. Our results demonstrate that for larger system bath coupling strengths, full polaron based quantum master equation is unable to provide accurate results whereas for weaker system bath coupling strengths, it performs better. Further, for a given system bath coupling strength, as logarithmic perturbations are increasing, the damping characteristics of the coherent energy transfer are also increasing. In addition, we show that smaller values of the Ohmicity parameter can suffer severe distortions even for a small logarithmic perturbation. Doing so, we show that full polaron transformation-based quantum master equation is capable of undergoing infrared divergence even for a super Ohmic environment, when higher orders logarithmic perturbations are present.