Quantum dynamics in strong fluctuating fields

A large number of multifaceted quantum transport processes in molecular systems and physical nanosystems, such as e.g. nonadiabatic electron transfer in proteins, can be treated in terms of quantum relaxation processes which couple to one or several fluctuating environments. A thermal equilibrium environment can conveniently be modelled by a thermal bath of harmonic oscillators. An archetype situation provides a two-state dissipative quantum dynamics, commonly known under the label of a spin-boson dynamics. An interesting and nontrivial physical situation emerges, however, when the quantum dynamics evolves far away from thermal equilibrium. This occurs, for example, when a charge transferring medium possesses nonequilibrium degrees of freedom, or when a strong time-dependent control field is applied externally. Accordingly, certain parameters of underlying quantum subsystem acquire stochastic character. This may occur, for example, for the tunnelling coupling between the donor and acceptor states of the transferring electron, or for the corresponding energy difference between electronic states which assume via the coupling to the fluctuating environment an explicit stochastic or deterministic time-dependence. Here, we review the general theoretical framework which is based on the method of projector operators, yielding the quantum master equations for systems that are exposed to strong external fields. This allows one to investigate on a common basis, the influence of nonequilibrium fluctuations and periodic electrical fields on those already mentioned dynamics and related quantum transport processes. Most importantly, such strong fluctuating fields induce a whole variety of nonlinear and nonequilibrium phenomena. A characteristic feature of such dynamics is the absence of thermal (quantum) detailed balance. Contents PAGE 1. Introduction 526 2. Quantum dynamics in stochastic fields 531 2.1. Stochastic Liouville equation 531 2.2. Non-Markovian vs. Markovian discrete state fluctuations 531 2.3. Averaging the quantum propagator 533 2.3.1. Kubo oscillator 535 2.3.2. Averaged dynamics of two-level quantum systems exposed to two-state stochastic fields 537 2.4. Projection operator method: a primer 540 3. Two-state quantum dynamics in periodic fields 542 3.1. Coherent destruction of tunnelling 542 3.2. Driving-induced tunnelling oscillations (DITO) 543 4. Dissipative quantum dynamics in strong time-dependent fields 544 4.1. General formalism 544 4.1. 1. Weak-coupling approximation 545 4.1. 2. Markovian approximation: Generalised Redfield Equations 547 5. Application I: Quantum relaxation in driven, dissipative two-level systems 548 5.1. Decoupling approximation for fast fluctuating energy levels 550 5.1. 1. Control of quantum rates 551 5.1. 2. Stochastic cooling and inversion of level populations 552 5.1. 3. Emergence of an effective energy bias 553 5.2. Quantum relaxation in strong periodic fields 554 5.3. Approximation of time-dependent rates 554 5.4. Exact averaging for dichotomous Markovian fluctuations 555 6. Application II: Driven electron transfer within a spin-boson description 557 6.1. Curve-crossing problems with dissipation 558 6.2. Weak system-bath coupling 559 6.3. Beyond weak-coupling theory: Strong system-bath coupling 563 6.3.1. Fast fluctuating energy levels 565 6.3.2. Exact averaging over dichotomous fluctuations of the energy levels 566 6.3. 3. Electron transfer in fast oscillating periodic fields 567 6.3. 4. Dichotomously fluctuating tunnelling barrier 568 7. Quantum transport in dissipative tight-binding models subjected to strong external fields 569 7.1. Noise-induced absolute negative mobility 571 7.2. Dissipative quantum rectifiers 573 7.3. Limit of vanishing dissipation 575 7.4. Case of harmonic mixing drive 575 8. Summary 576 Acknowledgements 578 References 579