The hierarchical equations of motion (HEOM) method has recently been widely applied to many problems of quantum dynamics in condensed phase. It is now well known that the auxiliary density operators (ADOs) in the HEOM formalism contain system-bath correlations that are important in calculating various dynamical properties, yet quantitative relations to explicitly calculate such correlations from the ADOs are still scarce. This paper extends a previous study [Q. Shi et al., J. Chem. Phys. 130, 164518 (2009)10.1063/1.3125003] in investigating the physical meaning of ADOs to general spectral densities and lower temperature cases. Using the path-integral technique, we derive exact relations between the expectation values of the collective bath coordinate and the ADOs, which could be very useful in investigating the correlated system-bath dynamics directly with the HEOM formalism. Numerical examples concerning the evolution of the expectation values of the collective bath coordinate are also presented.

Explicit system-bath correlation calculated using the hierarchical equations of motion method.

Ultrafast photoinduced intermolecular electron transfer (ET) dynamics involving 7-aminocoumarin derivatives as electron donor and pyridinium moiety of surfactant molecules in cetylpyridinium chloride (CPC) micelle as electron acceptor has been investigated to understand the role of separation and orientation of reactants on micellar ET reactions. Unlike in noninteracting micelles (like Triton-X-100, sodium dodecyl sulfate, dodecyltrimethylammonium bromide, etc.), where surfactant-separated donor−acceptor pairs are understood to give the ultrafast ET component with the shortest time constant in the range of ∼4 ps, in CPC micelles with pyridinium moiety as the intrinsic acceptor the ultrafast ET component is found to be in the subpicosecond time scale (of around 240 fs). This time scale is very similar to the values reported in the cases of ultrafast ET reactions involving coumarin dyes in electron-donating solvents. The ultrafast ET times in CPC micelles are significantly faster than the diffusive solvatio...

Ultrafast Electron Transfer Dynamics in Micellar Media Using Surfactant as the Intrinsic Electron Acceptor

We rigorously investigate the quantum dissipative dynamics of a ratchet system described by a periodic potential model based on the Caldeira-Leggett Hamiltonian with a biharmonic force. In this model, we use the reduced hierarchy equations of motion in the Wigner space representation. These equations represent a generalization of the Gaussian-Markovian quantum Fokker-Planck equation introduced by Tanimura and Wolynes (1991), which was formulated to study non-Markovian and non-perturbative thermal effects at finite temperature. This formalism allows us to treat both the classical limit and the tunneling regimes, and it is helpful for identifying purely quantum mechanical effects through the time evolution of the Wigner distribution. We carried out extensive calculations of the classical and quantum currents for various temperatures, coupling strengths, and barrier heights. Our results reveal that at low temperature, while the quantum current is larger than the classical current in the case of a high barrier, the opposite is true in the case of a low barrier. We find that this behavior results from the fact that the tunneling enhances the current in the case of a high barrier, while it suppresses the current in the case of a low barrier. This is because the effect of the ratchet potential is weak in the case of a low barrier, due to the large dispersion of the distribution introduced by tunneling. This causes the spatio-temporal asymmetry, which is necessary for ratchet current, to be weak, and as a result, the net current is suppressed.

/pdf/quantum-suppression-of-ratchet-rectification-in-a-brownian-g5f0waklgq.pdf

Quantum Suppression of Ratchet Rectification in a Brownian System Driven by a Biharmonic Force

The quantum dissipative dynamics of a tunneling process through double barrier structures is investigated on the basis of non-perturbative and non-Markovian treatment. We employ a Caldeira?Leggett Hamiltonian with an effective potential calculated self-consistently, accounting for the electron distribution. With this Hamiltonian, we use the reduced hierarchy equations of motion in the Wigner space representation to study non-Markovian and non-perturbative thermal effects at finite temperature in a rigorous manner. We study current variation in time and the current?voltage (I?V ) relation of the resonant tunneling diode for several widths of the contact region, which consists of doped GaAs. Hysteresis and both single and double plateau-like behavior are observed in the negative differential resistance (NDR) region. While all of the current oscillations decay in time in the NDR region in the case of a strong system?bath coupling, there exist self-excited high-frequency current oscillations in some parts of the plateau in the NDR region in the case of weak coupling. We find that the effective potential in the oscillating case possesses a basin-like form on the emitter side (emitter basin) and that the current oscillation results from tunneling between the emitter basin and the quantum well in the barriers. We find two distinct types of current oscillations, with large and small oscillation amplitudes, respectively. These two types of oscillation appear differently in the Wigner space, with one exhibiting tornado-like motion and the other exhibiting a two piston engine-like motion.

/pdf/self-excited-current-oscillations-in-a-resonant-tunneling-14qljexu5y.pdf

Self-excited current oscillations in a resonant tunneling diode described by a model based on the Caldeira–Leggett Hamiltonian

We introduce a simple and flexible method to generate spatially non-Markovian light with tunable coherence properties in one and two dimensions. The unusual behavior of this light is demonstrated experimentally by probing the far field and by recording its diffraction pattern after a double slit: In both cases we observe, instead of a central intensity maximum, a line- or cross-shaped dark region, whose width and profile depend on the non-Markovian coherence properties. Because these properties can be controlled and easily reproduced in experiment, the presented approach lends itself to serving as a test bed to study and gain a deeper understanding of non-Markovian processes.

/pdf/light-with-tunable-non-markovian-phase-imprint-2zvms80x4m.pdf

Light with Tunable Non-Markovian Phase Imprint

While the exact theory of chemical reaction rate processes is always non-Markovian, experimental rates do often show practically Markovian that supports kinetics rate constant description. In this work, we propose to use the Kubo's motional narrowing line shape function to characterize the Markovian character of the simplest two-state electron transfer reaction system. On the basis of analytical results, we demonstrate the related Markovianicity parameter as an interplay between the fluctuating solvent environment and the coherent transfer coupling. It is found that a non-Markovian rate process is most likely to occur in a symmetric system in the fast solvent modulation regime, where the resonant tunneling enhancement plays the important role. The effect of quantum solvation on electron transfer, which is dominant in the fast modulation regime, will also be highlighted.

Electron Transfer Theory Revisit: Motional Narrowing Induced Non-Markovian Rate Processes

In this work, we revisit the electron-transfer rate theory, with particular interests in the distinct quantum solvation effect and the characterizations of adiabatic/nonadiabatic and Markovian/non-Markovian rate processes. We first present a full account for the quantum solvation effect on the electron transfer in Debye solvents, addressed previously in J. Theor. Comput. Chem. 2006, 5, 685. Distinct reaction mechanisms, including the quantum solvation-induced transitions from barrier crossing to tunneling and from barrierless to quantum barrier crossing rate processes, are shown in the fast modulation or low viscosity regime. This regime is also found in favor of nonadiabatic rate processes. We further propose to use Kubo's motional narrowing line shape function to describe the Markovian character of the reaction. It is found that a non-Markovian rate process is most likely to occur in a symmetric system in the fast modulation regime, where the electron transfer is dominant by tunneling due to the Fermi r...

The quantum solvation, adiabatic versus nonadiabatic, and Markovian versus non-Markovian nature of electron-transfer rate processes.

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Electron Transfer Theory Revisit: Motional Narrowing Induced Non-Markovian Rate Processes

The quantum solvation, adiabatic versus nonadiabatic, and Markovian versus non-Markovian nature of electron-transfer rate processes.