Previously derived expressions for the characteristic function of work performed on a quantum system by a classical external force are generalized to arbitrary initial states of the considered system and to Hamiltonians with degenerate spectra. In the particular case of microcanonical initial states, explicit expressions for the characteristic function and the corresponding probability density of work are formulated. Their classical limit as well as their relations to the corresponding canonical expressions are discussed. A fluctuation theorem is derived that expresses the ratio of probabilities of work for a process and its time reversal to the ratio of densities of states of the microcanonical equilibrium systems with corresponding initial and final Hamiltonians. From this Crooks-type fluctuation theorem a relation between entropies of different systems can be derived which does not involve the time-reversed process. This entropy-from-work theorem provides an experimentally accessible way to measure entropies.

We study, within the spin-boson dynamics, the synchronization of a quantum tunneling system with an external, time-periodic driving signal. As a main result, we find that at a sufficiently large system-bath coupling strength (i.e., for a friction strength > 1) the thermal noise plays a constructive role in yielding forced synchronization. This noise-induced synchronization can occur when the driving frequency is larger than the zero-temperature tunneling rate. As an application evidencing the effect, we consider the charge transfer dynamics in molecular complexes. DOI: 10.1103/PhysRevLett.97.210601 PACS numbers: 05.60.Gg, 05.40.ÿa, 05.45.Xt, 82.20.Gk The study of the different versions of synchronization appearing in nonlinear classical systems has gained importance over the past decade [1][2][3][4]. A special class of problems is provided by noise-induced forced synchronization in driven bistable nonlinear systems [2,5,6]. Here a stochastic phase process can be associated with the jumping events between two domains of attraction. The locking of the average frequency of the phase process to that of the external driving and the smallness of the phase-diffusion coefficient in a corresponding interval of noise strengths are the fingerprints of such noise-induced forced synchronization [7][8][9]. Another manifestation of the rich dynamics of such systems is stochastic resonance (SR) [10], which recently has been generalized to the quantum regime [11][12][13]. Its experimental realization on the level of a nanomechanical quantum memory element is now feasible [14]. Although synchronization and SR are related, the existence of SR does not necessarily imply a (phase) synchronization, as emphasized in Ref. [5]. The extension of noiseinduced synchronization into the realm of quantum physics has not been considered thus far. This latter task presents a challenge which, apart from prominent academic interest, also comprises a great potential for nanoscience with beneficial applications ranging from quantum control to quantum information processing. With this work, we undertake a first step in this direction.Dissipative quantum tunneling changes radically the physics of classical synchronization. At zero temperature, the system can only tunnel towards its lowest energy state when a biasing dc signal is applied. As the bias periodically changes its sign due to the action of a driving field, tunneling causes the particle to move periodically towards its corresponding lowest energy state, as long as the driving period is much longer than the typical time scale for tunneling. Consequently, one expects that the system may synchronize when driven by a periodic, e.g., rectangular-shaped, signal. By contrast, in the absence of thermal noise, synchronization in overdamped classical bistable systems driven by subthreshold signals fails as no overbarrier transitions occur.Two interesting questions now emerge: What is the effect of the generally deteriorating thermal quantum noise at finite temperatures on synchronization? How does...

In the context of the phenomenon of Stochastic Resonance (SR) we study the correlation function, the signal-to-noise ratio (SNR) and the ratio of output over input SNR, i.e. the gain, which is associated to the nonlinear response of a bistable system driven by time-periodic forces and white Gaussian noise. These quantifiers for SR are evaluated using the techniques of Linear Response Theory (LRT) beyond the usually employed two-mode approximation scheme. We analytically demonstrate within such an extended LRT description that the gain can indeed not exceed unity.We implement an efficient algorithm, based on work by Greenside and Helfand (detailed in the Appendix), to integrate the driven Langevin equation over a wide range of parameter values. The predictions of LRT are carefully tested against the results obtained from numerical solutions of the corresponding Langevin equation over a wide range of parameter values. We further present an accurate procedure to evaluate the distinct contributions of the coherent and incoherent parts of the correlation function to the SNR and the gain. As a main result we show for subthreshold driving that both, the correlation function and the SNR can deviate substantially from the predictions of LRT and yet, the gain can be either larger or smaller than unity. In particular, we find that the gain can exceed unity in the strongly nonlinear regime which is characterized by weak noise and very slow multifrequency subthreshold input signals with a small duty cycle. This latter result is in agreement with recent analogue simulation results by Gingl et al. in Refs. [18,19].

We present a theory of solvent effects on the rate of intramolecular proton-transfer (IPT) reactions. The proton tunnels between two vibrational levels of a double minimum potential. The proton’s coupling to the solvent is modeled with an oscillator bath, appropriate to reactions where a charge interacts with many solvent molecules. The rate is evaluated by use of the Golden Rule; the perturbation is the level splitting. The IPT rate constant has several limiting expressions, one of which has an activated form. The activation energy is related to the medium reorganization energy, and provides a mechanism to slow the IPT reaction. Since reorganization energies are small in nonpolar and large in polar solvents, the rate is expected to be smaller in the latter class of solvents. Isotopic substitution is predicted to only affect the prefactor of the rate expression. Another regime is obtained for smaller reorganization energies where the solvent dynamics, as described by a dielectric relaxation time, are important. Comparison is made with recent experimental studies of IPT in solution.

The possibility of controlling the tunneling of a proton in a condensed phase with the use of static or time varying external fields, which couple to the transition dipole moment of the tunneling proton, is investigated. Starting from a Hamiltonian, an equation of motion describing the tunnel dynamics of the proton as a stochastically modulated, externally driven, two-level system is derived under suitable restrictions. For external fields that satisfy a precise connection between frequency and amplitude, whereby the resulting Floquet eigenvalues (quasienergies) are degenerate, tunneling can be suppressed in the absence of the medium. With the medium present, we examine the consequences to this tunnel suppression. Static fields, if sufficiently strong, can also suppress tunneling. Expressions are derived for the effect of a static external field on the medium-influenced, tunnel-rate constant. The rate constant can be enhanced or decreased, depending on the sizes of the medium-reorganization energy and external field and the latter's direction relative to the tunnel system. It is demonstrated that proton tunneling in dicarboxylic acids would be a good candidate to exhibit a proton-transfer rate dependent on the relative orientation of the external field and proton tunnel system. 4548