Jianshu Cao

The formulation of quantum statistical mechanics based on the Feynman path centroid density. II. Dynamical properties

The formulation of quantum dynamical time correlation functions is examined within the context of the path centroid variable in Feynman path integration. This study builds on the centroid‐based approach to equilibrium properties developed in the companion paper. The introduction of the centroid perspective into the calculation of real time position correlation functions is outlined and an intriguing quasiclassical role for the centroid variable in real time position correlation functions is identified. This quasiclassical perspective is developed in terms of general interaction potentials, and the computational effort in implementing the method should scale with the size of the system in the same fashion as a classical molecular dynamics calculation. The centroid‐based theory is also implemented in several different approaches to calculate general time correlation functions. The theoretical results are illustrated and tested by representative numerical applications.

The formulation of quantum statistical mechanics based on the Feynman path centroid density. IV. Algorithms for centroid molecular dynamics

Numerical algorithms are developed for the centroid molecular dynamics (centroid MD) method to calculate dynamical time correlation functions for general many‐body quantum systems. Approaches based on the normal mode path integral molecular dynamics and staging path integral Monte Carlo methods are described to carry out a direct calculation of the force on the centroid variables in the centroid MD algorithm. A more efficient, but approximate, scheme to compute the centroid force is devised which is based on the locally optimized harmonic approximation for the centroid potential. The centroid MD equations in the latter method can be solved with the help of an iterative procedure or through extended Lagrangian dynamics. A third algorithm introduces an effective centroid pseudopotential to approximate the full many‐body centroid mean force potential by effective pairwise centroid interactions. Numerical simulations for both prototype models and more realistic many‐body systems are performed to explore the f...

The formulation of quantum statistical mechanics based on the Feynman path centroid density. III. Phase space formalism and analysis of centroid molecular dynamics

The formulation of quantum statistical mechanics based on the path centroid variable in Feynman path integration is generalized to a phase space perspective, thereby including the momentum as an independent dynamical variable. By virtue of this approach, operator averages and imaginary time correlation functions can be expressed in terms of an averaging over the multidimensional phase space centroid density. The imaginary time centroid‐constrained correlation function matrix for the phase space variables is then found to define the effective thermal width of the phase space centroid variable. These developments also make it possible to rigorously analyze the centroid molecular dynamics method for computing quantum dynamical time correlation functions. As a result, the centroid time correlation function as calculated from centroid molecular dynamics is shown to be a well‐defined approximation to the exact Kubo transformed position correlation function. This analysis thereby clarifies the underlying role of the equilibrium path centroid variable in the quantum dynamical position correlation function and provides a sound theoretical basis for the centroid molecular dynamics method.

A new perspective on quantum time correlation functions

A theoretical analysis suggests that the path centroid variable in Feynman path integration occupies a central role in the behavior of the real time position autocorrelation function. Based on this analysis, an intriguing quasiclassical perspective on quantum correlation functions emerges.

Efficient energy transfer in light-harvesting systems, I: optimal temperature, reorganization energy and spatial–temporal correlations

Understanding the mechanisms of efficient and robust energy transfer in light-harvesting systems provides new insights for the optimal design of artificial systems. In this paper, we use the Fenna-Matthews-Olson (FMO) protein complex and phycocyanin 645 (PC 645) to explore the general dependence on physical parameters that help maximize the efficiency and maintain its stability. With the Haken-Strobl model, the maximal energy transfer efficiency (ETE) is achieved under an intermediate optimal value of dephasing rate. To avoid the infinite temperature assumption in the Haken-Strobl model and the failure of the Redfield equation in predicting the Forster rate behavior, we use the generalized Bloch-Redfield (GBR) equation approach to correctly describe dissipative exciton dynamics, and we find that maximal ETE can be achieved under various physical conditions, including temperature, reorganization energy and spatial-temporal correlations in noise. We also identify regimes of reorganization energy where the ETE changes monotonically with temperature or spatial correlation and therefore cannot be optimized with respect to these two variables.

Optimization of Exciton Trapping in Energy Transfer Processes

In this paper, we establish optimal conditions for maximal energy transfer efficiency using solutions for multilevel systems and interpret these analytical solutions with more intuitive kinetic networks resulting from a systematic mapping procedure. The mapping procedure defines an effective hopping rate as the leading order picture and nonlocal kinetic couplings as the quantum correction, hence leading to a rigorous separation of thermal hopping and coherent transfer useful for visualizing pathway connectivity and interference in quantum networks. As a result of these calculations, the dissipative effects of the surrounding environments can be optimized to yield the maximal efficiency, and modulation of the efficiency can be achieved using the cumulative quantum phase along any closed loops. The optimal coupling of the system and its environments is interpreted with the generic mechanisms: (i) balancing localized trapping and delocalized coherence, (ii) reducing the effective detuning via homogeneous line-broadening, (iii) suppressing the destructive interference in nonlinear network configurations, and (iv) controlling phase modulation in closed loop configurations. Though these results are obtained for simple model systems, the physics thus derived provides insights into the working of light harvesting systems, and the approaches thus developed apply to large-scale computation.

Adiabatic path integral molecular dynamics methods. II. Algorithms

Efficient numerical algorithms are developed for use with two finite temperature semiclassical approximations to quantum dynamics both of which require trajectories generated on potentials of mean force derived from the path integral expression for the density matrix. The numerical algorithms are formed from the combination of a classical adiabatic relation similar to that used in the Car–Parrinello method and an efficient path integral molecular dynamics scheme. Results on model, an anharmonic oscillator and a realistic, fluid para‐hydrogen, problem indicate that semiclassical dynamics can be obtained for virtually the same computational cost as structure and thermodynamics.

The formulation of quantum statistical mechanics based on the Feynman path centroid density. V. Quantum instantaneous normal mode theory of liquids

The concept of instantaneous normal modes in liquids is extended into the quantum regime using the Feynman path centroid perspective in quantum statistical mechanics. To accomplish this goal, the variational quadratic approximation for the effective centroid potential is recast in a general multidimensional phase space form. In the context of the effective quadratic approximation, the velocity autocorrelation functions of liquids can then be predicted based on a set of instantaneous quantum normal modes. Representative applications are presented for quantum Lennard‐Jones liquids and a quantum particle solvated in a classical fluid. The quantum effective phonon spectrum leads to some revealing observations and interpretations for these systems.

On energy estimators in path integral Monte Carlo simulations: Dependence of accuracy on algorithm

Two energy estimators, the Barker estimator and the Berne virial estimator, commonly used in path integral simulations of quantum systems are compared with respect to statistical accuracy. It is found that the accuracy of these estimators is strongly affected by the algorithm used. Four common algorithms are considered here:  (1) the pure primitive algorithm, (2) the primitive algorithm augmented by whole chain moves, (3) the normal‐mode algorithm, and (4) the staging algorithm. The error of the mean of the Barker energy estimator is found to grow as (P)1/2, where P is the number of discretization points of the quantum paths (or the number of chain particles in the isomorphic classical chain), for all of the algorithms above. The error of the mean of the Berne virial energy estimator is independent of P for algorithms 2, 3, and 4, and increases as (P)1/2 for algorithm 1. It is concluded that the virial estimator is far more accurate than the Barker estimator for algorithms 2, 3, and 4, and is at least as accurate for algorithm 1. Because the error analysis depends strongly on the temporal correlations in the sequence of values of the energy estimator generated during Monte Carlo or molecular‐dynamics simulations, we review the general question of error analysis in simulations.

Event-averaged measurements of single-molecule kinetics

Abstract A modulated N-conformational-channel reactive system is used to model the recent single-molecule enzymatic experiment [Science 282 (1998) 1877]. Kinetic analysis of the model system clearly demonstrates the essential difference between ensemble-averaged bulk measurements associated with the population dynamics of full-reactions and event-averaged single-molecule measurements associated with a sequence of half-reactions. Example calculations of a two-conformational-channel system support the principal findings of the reported experiment. In particular, the observation of the focal time in the single-event distribution function and the echo signal in the two-event distribution function reveals the nature of conformational landscapes.