Advancing Hierarchical Equations of Motion for Efficient Evaluation of Coherent Two-dimensional Spectroscopy

To advance hierarchical equations of motion as a standard theory for quantum dissipative dynamics, we put forward a mixed Heisenberg-SchrSdinger scheme with block-matrix implementation on efficient evaluation of nonlinear optical response function. The new approach is also integrated with optimized hierarchical theory and numerical filtering algorithm. Different configurations of coherent two-dimensional spectroscopy of model excitonic dimer systems are investigated, with focusing on the effects of intermolecular transfer coupling and bi-exciton interaction.

Adiabatic Terminator for Fermionic Hierarchical Equations of Motion

The hierarchical equation of motion method has become one of the most popular numerical methods for describing the dissipative dynamics of open quantum systems linearly coupled to environment.However,its applications to systems with strong electron correlation are largely restrained by the computational cost,which is mainly caused by the high truncation tier L required to accurately characterize the strong correlation effect.In this work,we develop an adiabatic terminator by decoupling the principal dissipation mode with the fastest dissipation rate from the slower ones.The adiabatic terminator leads to substantially enhanced convergence with respect to L as demonstrated by the numerical tests carried out on a single impurity Anderson model.Moreover,the adiabatic terminator alleviates the numerical instability problems in the long-time dissipative dynamics.

Mixed Quantum Classical Reaction Rates based on the Phase Space Formulation of the Hierarchical Equations of Motion

In a previous work[J.Chem.Phys.140,174105(2014)],we have shown that a mixed quantum classical(MQC)rate theory can be derived to investigate the quantum tunneling effects in the proton transfer reactions.However,the method is based on the high temperature approximation of the hierarchical equation of motion(HEOM)with the Debye-Drude spectral density,and results in a multistate Zusman type of equation.We now extend this theory to include quantum effects of the bath degrees of freedom.By writing the full HEOM into a multidimensional partial differential equation in phase space,we can define a new reaction coordinate,and the previous method can be generalized to the full quantum regime.The validity of the new method is demonstrated by using numerical examples,including the spin-Boson model,and the double well model for proton transfer reaction.The new method is found to resolve some key problems of the previous theory based on high temperature approximation,including possible numerical instability in long time simulation and wrong rate constant at low temperatures.

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.