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The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature approximation of the hierarchical theory is equivalent to the Zusman equation in describing electron transfer dynamics. Thus the exact hierarchical formalism naturally extends the Zusman equation to include quantum nuclear dynamics at low temperatures. This new finding has also inspired us to rescale the original hierarchical equations and incorporate a filtering algorithm to efficiently propagate the hierarchical equations. Numerical exact results are also presented for the electron transfer reaction dynamics and rate constant calculations. [ABSTRACT FROM AUTHOR]

The theory of optimal control together with that of transient probe absorption spectroscopy are applied for control and detection of molecular wave packet dynamics in the weak response regime. We obtain a globally optimal pump-dump control field which drives the initial state to the predefined target, focused at the inner-turning point region of the electronic ground state potential. As for the detection, we calculate both the integrated and the dispersed transient pump-dumpprobe absorption signals and adopt the difference detection schemes to reveal the optimally controlled molecular dynamics. [ABSTRACT FROM AUTHOR]

A quantum dissipation theory is constructed with the system-bath interaction being treated rigorously at the second-order cumulant level for both reduced dynamics and initial canonical boundary condition. The theory is valid for arbitrary bath correlation functions and time-dependent external driving fields, and satisfies correlated detailed-balance relation at any temperatures. The general formulation assumes a particularly simple form in driven Brownian oscillator systems in which the correlated driving-dissipation effects can be accounted for exactly in terms of local-field correction. Remarks on a class of widely used phenomenological quantum master equations that neglects the bath dispersion-induced dissipation are also made in contact with the present theory. [ABSTRACT FROM AUTHOR]

By using a rather simple algebraic approach, we revisit and further bridge between two most commonly used quantum dissipation theories, the Bloch-Redfield theory and a class of Fokker-Planck equations. The nature of the common approximation scheme involving in these two theories is analyzed in detail. While the Bloch-Redfield theory satisfies the detailed-balance relation, we also construct a class of Fokker-Planck equations that satisfy the detailed-balance relation up to the second moments in phase-space. Developed is also a generalized Fokker-Planck equation that preserves the general positivity of the reduced density operator. Both T[sub 1]-relaxation and pure-T[sub 2] dephasing are considered, and their temperature dependence is shown to be very different. Provided is also an analogy between the quantum pure-T[sub 2] dephasing and the classical heat transport. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Several recent advancements for the hierarchical equations of motion (HEOM) approach are reported. First, we propose an a priori estimate for the optimal number of basis functions for the reservoir memory decomposition. Second, we make use of the sparsity of auxiliary density operators (ADOs) and propose two ansatzs to screen out all the intrinsic zero ADO elements. Third, we propose a new truncation scheme by utilizing the time derivatives of higher-tier ADOs. These novel techniques greatly reduce the memory cost of the HEOM approach, and thus enhance its efficiency and applicability. The improved HEOM approach is applied to simulate the coherent dynamics of Aharonov-Bohm double quantum dot interferometers. Quantitatively accurate dynamics is obtained for both noninteracting and interacting quantum dots. The crucial role of the quantum phase for the magnitude of quantum coherence and quantum entanglement is revealed.

An optimal control theory for open quantum systems is constructed containing non-Markovian dissipation manipulated by an external control field. The control theory is developed based on a novel quantum dissipation formulation that treats both the initial canonical ensemble and the subsequent reduced control dynamics. An associated scheme of backward propagation is presented, allowing the efficient evaluation of general optimal control problems. As an illustration, the control theory is applied to the vibration of the hydrogen fluoride molecule embedded in a non-Markovian dissipative medium. The importance of control-dissipation correlation is evident in the results., ((c) 2004 American Institute of Physics)