Exciton–vibrational coupling in the dynamics and spectroscopy of Frenkel excitons in molecular aggregates

Photosynthetic bacteria, algae, and plants convert solar energy into biochemical fuel via light-harvesting complexes comprised of proteins and pigments. Pigments absorb photons by exciting electron-hole pairs that move readily to other pigments. How biology utilizes such quantum processes at room temperature to achieve efficiency of energy transfer is of interest to physicists. This article reviews computational and spectroscopic advances in understanding the energy conversion and energy transport of such a magnificent nanorectenna.

Delocalized excitons in natural light-harvesting complexes

A hierarchical equations of motion based numerical approach is developed for accurate and efficient evaluation of dynamical observables of strongly correlated quantum impurity systems. This approach is capable of describing quantitatively Kondo resonance and Fermi-liquid characteristics, achieving the accuracy of the latest high-level numerical renormalization group approach, as demonstrated on single-impurity Anderson model systems. Its application to a two-impurity Anderson model results in differential conductance versus external bias, which correctly reproduces the continuous transition from Kondo states of individual impurity to singlet spin states formed between two impurities. The outstanding performance on characterizing both equilibrium and nonequilibrium properties of quantum impurity systems makes the hierarchical equations of motion approach potentially useful for addressing strongly correlated lattice systems in the framework of dynamical mean-field theory.

Hierarchical Liouville-Space Approach for Accurate and Universal Characterization of Quantum Impurity Systems

This work establishes a strongly correlated system-and-bath dynamics theory, the many-dissipaton density operators formalism. It puts forward a quasi-particle picture for environmental influences. This picture unifies the physical descriptions and algebraic treatments on three distinct classes of quantum environments, electron bath, phonon bath, and two-level spin or exciton bath, as their participating in quantum dissipation processes. Dynamical variables for theoretical description are no longer just the reduced density matrix for system, but remarkably also those for quasi-particles of bath. The present theoretical formalism offers efficient and accurate means for the study of steady-state (nonequilibrium and equilibrium) and real-time dynamical properties of both systems and hybridizing environments. It further provides universal evaluations, exact in principle, on various correlation functions, including even those of environmental degrees of freedom in coupling with systems. Induced environmental dynamics could be reflected directly in experimentally measurable quantities, such as Fano resonances and quantum transport current shot noise statistics.

Theory of open quantum systems with bath of electrons and phonons and spins: many-dissipaton density matrixes approach.

Accurate characterization of correlated electronic states, as well as their evolution under external fields or in dissipative environment, is essentially important for understanding the properties of strongly correlated transition-metal materials involving spin-unpaired d or f electrons. This paper reviews the development and applications of a numerical simulation program, the Hierarchical Equations of Motion for QUantum Impurity with a Correlated Kernel (HEOM-QUICK), which allows for an accurate and universal characterization of strongly correlated quantum impurity systems. The HEOM-QUICK program implements the formally exact HEOM formalism for fermionic open systems. Its simulation results capture the combined effects of system-environment dissipation, many-body interactions, and non-Markovian memory in a nonperturbative manner. The HEOM-QUICK program has been employed to explore a wide range of static and dynamic properties of various types of quantum impurity systems, including charge or spin qubits, quantum dots, molecular junctions, and so on. It has also been utilized in conjunction with first-principles methods such as density-functional theory methods to study the correlated electronic structure of adsorbed magnetic molecules. The advantages in its accuracy, efficiency, and universality have made the HEOM-QUICK program a reliable and versatile tool for theoretical investigations on strong electron correlation effects in complex materials. WIREs Comput Mol Sci 2016, 6:608–638. doi: 10.1002/wcms.1269

For further resources related to this article, please visit the WIREs website.

HEOM-QUICK: a program for accurate, efficient, and universal characterization of strongly correlated quantum impurity systems

In the mesoscopic world the nano-structured environment is not just of quantum in nature but also often nonperturbative and non-Markovian for its influence on the system of primary interest. In this talk, I will discuss the hierarchical equations of motion (HEOM) approach [1–4] that can be considered as a fundamental formalism in quantum mechanics of dissipative and open systems. HEOM is formally equivalent to such as the Feynman-Vernon influence functional and nonequilibrium many-body Green’s function formalisms [5], but numerically more implementable. It provides a unified treatment of various decoherence and quantum transport processes. It renders also a unified view on various existing approximated theories, such as the quantum master equation and stochastic Liouville equation [6], and consequently, often further results in some simple but important modifications to those conventional approximations [7]. I will also discuss about two recent developments, the best/minimum stochastic environment basis set for optimal HEOM construction [8] and the efficient on-the-fly numerical filtering algorithm [9], that significantly enhance the numerical tractability of the exact HEOM dynamics. Numerical results on the 2D spectrum of a model light harvesting antenna system and the quantum transport through Anderson model quantum dots system will be presented.

/pdf/hierarchical-equations-of-motion-for-quantum-dissipation-and-qd2uncwppc.pdf

Jin Jinshuang

Papers

Hierarchical Equations of Motion for Quantum Dissipation and Quantum Transport