Generalized Quantum Master Equation:A Tutorial Review and Recent Advances

The generalized quantum master equation(GQME)provides a general and exact approach for simulating the reduced dynamics in open quantum systems where a quantum system is embedded in a quantum environment.Dynamics of open quantum systems is important in excitation energy,charge,and quantum coherence transfer as well as reactive photochemistry.The system is usually chosen to be the interested degrees of freedom such as the electronicstates in light-harvesting molecules or tagged vibrational modes in a condensed-phase system.The environment is also called the bath,whose influence on the system has to be considered,and for instance can be described by the GQME formalisms using the projection operator technique.In this review,we provide a heuristic description of the development of two canonical forms of GQME,namely the time-convoluted Nakajima-Zwanzig form(NZ-GQME)and the time-convolutionless form(TCL-GQME).In the more popular NZ-GQME form,the memory kernel serves as the essential part that reflects the non-Markovian and non-perturbative effects,which gives formally exact dynamics of the reduced density matrix.We summarize several schemes to express the projection-based memory kernel of NZ-GQME in terms of projection-free time correlation function inputs that contain molecular information.In particular,the recently proposed modified GQME approach based on NZ-GQME partitions the Hamiltonian into a more general diagonal and off-diagonal parts.The projection-free inputs in the above-mentioned schemes expressed in terms of different system-dependent time correlation functions can be calculated via numerically exact or approximate dynamical methods.We hope this contribution would help lower the barrier of understanding the theoretical pillars for GQME-based quantum dynamics methods and also envisage that their combination with the quantum computing techniques will pave the way for solving complex problems related to quantum dynamics and quantum information that are currently intractable even with today’s state-of-the-art classical supercomputers.

A fluctuation theorem for Floquet quantum master equations

We present a fluctuation theorem for Floquet quantum master equations. This is a detailed version of the famous Gallavotti–Cohen theorem. In contrast to the latter theorem, which involves the probability distribution of the total heat current, the former involves the joint probability distribution of positive and negative heat currents and can be used to derive the latter. A quantum two-level system driven by a periodic external field is used to verify this result.

On a tilted Liouville-master equation of open quantum systems

A tilted Liouville-master equation in Hilbert space is presented for Markovian open quantum systems.We demonstrate that it is the unraveling of the tilted quantum master equation.The latter is widely used in the analysis and calculations of stochastic thermodynamic quantities in quantum stochastic thermodynamics.

Tunneling Electrons Triggered Energy Transfer between Coherently Coupled Donor-Acceptor Molecules

Energy transfer is ubiquitous in natural and artificial lightharvesting systems,and coherent energy transfer,a highly efficient energy transfer process,has been accepted to play a vital role in such systems.However,the energy oscillation of coherent energy transfer is exceedingly difficult to capture because of its evanescence due to the interaction with a thermal environment.Here a microscopic quantum model is used to study the time evolution of electrons triggered energy transfer between coherently coupled donoracceptor molecules in scanning tunneling microscope(STM).A series of topics in the plasmonic nanocavity(PNC)coupled donor-acceptor molecules system are discussed,including resonant and nonresonant coherent energy transfer,dephasing assisted energy transfer,PNC coupling strength dependent energy transfer,Fano resonance of coherently coupled donor-acceptor molecules,and polariton-mediated energy transfer.

Coherent and incoherent theories for photosynthetic energy transfer

There is a remarkable characteristic of photosynthesis in nature, that is, the energy transfer efficiency is close to 100%. Recently, due to the rapid progress made in the experimental techniques, quantum coherent effects have been experimentally demonstrated. Traditionally, the incoherent theories are capable of calculating the energy transfer efficiency, e.g.,(generalized) F?rster theory and modified Redfield theory(MRT). However, in order to describe the quantum coherent effects in photosynthesis, one has to exploit coherent theories, such as hierarchical equation of motion(HEOM), quantum path integral, coherent modified Redfield theory(CMRT), small-polaron quantum master equation, and general Bloch-Redfield theory in addition to the Redfield theory. Here, we summarize the main points of the above approaches,which might be beneficial to the quantum simulation of quantum dynamics of exciton energy transfer(EET) in natural photosynthesis, and shed light on the design of artificial light-harvesting devices.