Low temperature electron transfer in strongly condensed phase

Quantum thermal transport beyond second order with the reaction coordinate mapping

Standard quantum master equation techniques, such as the Redfield or Lindblad equations, are perturbative to second order in the microscopic system–reservoir coupling parameter λ. As a result, the characteristics of dissipative systems, which are beyond second order in λ, are not captured by such tools. Moreover, if the leading order in the studied effect is higher-than-quadratic in λ, a second-order description fundamentally fails even at weak coupling. Here, using the reaction coordinate (RC) quantum master equation framework, we are able to investigate and classify higher-than-second-order transport mechanisms. This technique, which relies on the redefinition of the system–environment boundary, allows for the effects of system–bath coupling to be included to high orders. We study steady-state heat current beyond second-order in two models: The generalized spin-boson model with non-commuting system–bath operators and a three-level ladder system. In the latter model, heat enters in one transition and is extracted from a different one. Crucially, we identify two transport pathways: (i) System’s current, where heat conduction is mediated by transitions in the system, with the heat current scaling as j q ∝ λ2 to the lowest order in λ. (ii) Inter-bath current, with the thermal baths directly exchanging energy between them, facilitated by the bridging quantum system. To the lowest order in λ, this current scales as j q ∝ λ4. These mechanisms are uncovered and examined using numerical and analytical tools. We contend that the RC mapping brings, already at the level of the mapped Hamiltonian, much insight into transport characteristics.

Multilayer Multiconfiguration Time-Dependent Hartree Theory

Multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory is a rigorous and powerful method to simulate quantum dynamics in complex many-body systems. This approach extends the original MCTDH theory of Meyer, Manthe, and Cederbaum to include dynamically contracted layers in a recursive way, within which the equations of motion are determined from the Dirac-Frenkel variational principle. This paper presents the general derivation of the theory and analyzes the important features that make the ML-MCTDH method numerically efficient. Furthermore, we discuss the generalization of the theory to treat many-body identical particles (fermions or bosons) as well as calculating energy eigenstates via the improved relaxation method.

Golden rule kinetics of transfer reactions in condensed phase: the microscopic model of electron transfer reactions in disordered solid matrices

The algorithm for a theoretical calculation of transfer reaction rates for light quantum particles (i.e., the electron and H-atom transfers) in non-polar solid matrices is formulated and justified. The mechanism postulated involves a local mode (an either intra- or inter-molecular one) serving as a mediator which accomplishes the energy exchange between the reacting high-frequency quantum mode and the phonon modes belonging to the environment. This approach uses as a background the Fermi golden rule beyond the usually applied spin-boson approximation. The dynamical treatment rests on the one-dimensional version of the standard quantum relaxation equation for the reduced density matrix, which describes the frequency fluctuation spectrum for the local mode under consideration. The temperature dependence of a reaction rate is controlled by the dimensionless parameter ξ0 = ℏω0/k(B)T where ω0 is the frequency of the local mode and T is the temperature. The realization of the computational scheme is different for the high/intermediate (ξ0 < 1 - 3) and for low (ξ0 ≫ 1) temperature ranges. For the first (quasi-classical) kinetic regime, the Redfield approximation to the solution of the relaxation equation proved to be sufficient and efficient in practical applications. The study of the essentially quantum-mechanical low-temperature kinetic regime in its asymptotic limit requires the implementation of the exact relaxation equation. The coherent mechanism providing a non-vanishing reaction rate has been revealed when T → 0. An accurate computational methodology for the cross-over kinetic regime needs a further elaboration. The original model of the hopping mechanism for electronic conduction in photosensitive organic materials is considered, based on the above techniques. The electron transfer (ET) in active centers of such systems proceeds via local intra- and intermolecular modes. The active modes, as a rule, operate beyond the kinetic regimes, which are usually postulated in the existing theories of the ET. Our alternative dynamic ET model for local modes immersed in the continuum harmonic medium is formulated for both classical and quantum regimes, and accounts explicitly for the mode∕medium interaction. The kinetics of the energy exchange between the local ET subsystem and the surrounding environment essentially determine the total ET rate. The efficient computer code for rate computations is elaborated on. The computations are available for a wide range of system parameters, such as the temperature, external field, local mode frequency, and characteristics of mode/medium interaction. The relation of the present approach to the Marcus ET theory and to the quantum-statistical reaction rate theory [V. G. Levich and R. R. Dogonadze, Dokl. Akad. Nauk SSSR, Ser. Fiz. Khim. 124, 213 (1959); J. Ulstrup, Charge Transfer in Condensed Media (Springer, Berlin, 1979); M. Bixon and J. Jortner, Adv. Chem. Phys. 106, 35 (1999)] underlying it is discussed and illustrated by the results of computations for practically important target systems.

Escape rate for a quantum particle moving in a time-periodic rapidly oscillating potential: a time-independent approach

We explore, in the quantum regime, the stochastic dynamics of a time-periodic, rapidly oscillating potential (having a characteristic frequency of ω) within the framework of a time-dependent system-reservoir Hamiltonian. We invoke the idea of a quantum gauge transformation in light of the standard Floquet theorem in an attempt to construct a Langevin equation (bearing a time-independent effective potential) by employing a systematic perturbative expansion in powers of ω^{-1} using the natural time-scale separation. The time-independent effective potential (corrected to ω^{-2} in leading order) that acts on the slow motion of the driven particle can be employed for trapping. We proceed further to evaluate the rate of escape of the driven particle from the metastable state in the high-temperature limit. We also envisage a resonance phenomena, a true hallmark of the system-reservoir quantization. This development would thus serve as a model template to investigate the trapping mechanism, as well as an appropriate analog to understand the dynamics of a fluctuation-induced escape process from the trap.

Quantum Smoluchowski equation: a systematic study

The strong-friction regime at low temperatures is analyzed systematically starting from the formally exact path-integral expression for the reduced dynamics. This quantum Smoluchowski regime allows for a type of semiclassical treatment in the inverse friction strength so that higher-order quantum corrections to the original quantum Smoluchowski equation [J. Ankerhold, P. Pechukas, and H. Grabert, Phys. Rev. Lett. 87, 086802 (2001); J. Ankerhold and H. Grabert, Phys. Rev. Lett. 101, 119903 (2008)] can be derived. Drift and diffusion coefficients are determined by the equilibrium distribution in position and are directly related to the corresponding action of extremal paths and fluctuations around them. It is shown that the inclusion of higher-order corrections reproduces the quantum enhancement above crossover for the decay rate out of a metastable well exactly.

Quantum Brownian motion with large friction

Quantum Brownian motion in the strong friction limit is studied based on the exact path integral formulation of dissipative systems. In this limit the time-nonlocal reduced dynamics can be cast into an effective equation of motion, the quantum Smoluchowski equation. For strongly condensed phase environments it plays a similar role as master equations in the weak coupling range. Applications for chemical, mesoscopic, and soft matter systems are discussed and reveal the substantial role of quantum fluctuations.

Low temperature extension of the generalized Zusman phase space equations for electron transfer

In a previous paper [J. Chem. Phys. 119, 11864 (2003)], we derived a set of two coupled equations which describe electron transfer in the presence of dissipation at high temperature. Employing the low temperature extension of the Fokker-Planck operator, suggested by Haake and Reibold [Phys. Rev. A 32, 2462 (1985)] and Ankerhold [Europhys. Lett. 61, 301 (2003)], we show that one may extend the generalized Zusman equations in a similar manner to low temperature. Numerical simulation shows that addition of the temperature-dependent term which couples the coordinate and momentum causes an increase in the electron transfer rate as compared to the rate obtained from the previous high temperature equations. The increase in the rate comes from the increase in the equilibrium variances of the coordinate and momentum. The low temperature quantum theory allows for higher energy portions of phase space to contribute to the electron transfer rate where the rate is higher thus enhancing the overall rate.

Path-integral Monte Carlo simulations for electronic dynamics on molecular chains. I. Sequential hopping and super exchange

An improved real-time quantum Monte Carlo procedure is presented and applied to describe the electronic transfer dynamics along molecular chains. The model consists of discrete electronic sites coupled to a thermal environment which is integrated out exactly within the path integral formulation. The approach is numerically exact and its results reduce to known analytical findings (Marcus theory, golden rule) in proper limits. Special attention is paid to the role of superexchange and sequential hopping at lower temperatures in symmetric donor-bridge-acceptor systems. In contrast to previous approximate studies, superexchange turns out to play a significant role only for extremely high-lying bridges where the transfer is basically frozen or for extremely low temperatures where for weaker dissipation a description in terms of rate constants is no longer feasible. For bridges with increasing length an algebraic decrease of the yield is found for short as well as for long bridges. The approach can be extended to electronic systems with more complicated topologies including impurities and in presence of external time-dependent forces.