Strong coupling theory for tunneling and vibrational relaxation in driven bistable systems

A study of the dynamics of a tunneling particle in a driven bistable potential which is moderately-to-strongly coupled to a bath is presented. Upon restricting the system dynamics to the Hilbert space spanned by the M lowest energy eigenstates of the bare static potential, a set of coupled non-Markovian master equations for the diagonal elements of the reduced density matrix, within the discrete variale representation, is derived. The resulting dynamics is in good agreement with predictions of ab-initio real-time path integral simulations. Numerous results, analytical as well as numerical, for the quantum relaxation rate and for the asymptotic populations are presented. Our method is particularly convenient to investigate the case of shallow, time-dependent potential barriers and moderate-to-strong damping, where both a semi-classical and a Redfield-type approach are inappropriate.Comment: 37 pages, 23 figure

Relaxation time scales in collective dynamics of liquid alkali metals

In this paper the investigation of the dynamical processes of liquid alkali metals is executed by analyzing the time scales of relaxation processes in liquids. The obtained theoretical dynamic structure factor $S(k,\omega)$ for the case of liquid lithium is found to be in excellent agreement with the recently received inelastic X-ray scattering data. The comparison and interrelation with other theories are given here. Finally, an important part of this paper is the confirmation of the scale uniformity of the dynamic processes in liquid alkali metals predicted by some previous molecular dynamic simulation studies

Use and Abuse of a Fractional Fokker-Planck Dynamics for Time-Dependent Driving

We investigate a subdiffusive, fractional Fokker-Planck dynamics occurring in time-varying potential landscapes and thereby disclose the failure of the fractional Fokker-Planck equation (FFPE) in its commonly used form when generalized in an {\it ad hoc} manner to time-dependent forces. A modified FFPE (MFFPE) is rigorously derived, being valid for a family of dichotomously alternating force-fields. This MFFPE is numerically validated for a rectangular time-dependent force with zero average bias. For this case subdiffusion is shown to become enhanced as compared to the force free case. We question, however, the existence of any physically valid FFPE for arbitrary varying time-dependent fields that differ from this dichotomous varying family.Comment: 4 pages, 2 figure

Thermodynamics and Fluctuation Theorems for a Strongly Coupled Open Quantum System: An Exactly Solvable Case

We illustrate recent results concerning the validity of the work fluctuation theorem in open quantum systems [M. Campisi, P. Talkner, and P. H\"{a}nggi, Phys. Rev. Lett. {\bf 102}, 210401 (2009)], by applying them to a solvable model of an open quantum system. The central role played by the thermodynamic partition function of the open quantum system, -- a two level fluctuator with a strong quantum nondemolition coupling to a harmonic oscillator --, is elucidated. The corresponding quantum Hamiltonian of mean force is evaluated explicitly. We study the thermodynamic entropy and the corresponding specific heat of this open system as a function of temperature and coupling strength and show that both may assume negative values at nonzero low temperatures.Comment: 8 pages, 6 figure

Entropic transport - A test bed for the Fick-Jacobs approximation

Biased diffusive transport of Brownian particles through irregularly shaped, narrow confining quasi-one-dimensional structures is investigated. The complexity of the higher dimensional diffusive dynamics is reduced by means of the so-called Fick-Jacobs approximation, yielding an effective one-dimensional stochastic dynamics. Accordingly, the elimination of transverse, equilibrated degrees of freedom stemming from geometrical confinements and/or bottlenecks cause entropic potential barriers which the particles have to overcome when moving forward noisily. The applicability and the validity of the reduced kinetic description is tested by comparing the approximation with Brownian dynamics simulations in full configuration space. This non-equilibrium transport in such quasi-one-dimensional irregular structures implies for moderate-to-strong bias a characteristic violation of the Sutherland-Einstein fluctuation-dissipation relation.Comment: 15 pages, 6 figures ; Phil. Trans. R. Soc. A (2009), in pres

Universal Approach to Overcoming Nonstationarity, Unsteadiness and Non-Markovity of Stochastic Processes in Complex Systems

In present paper we suggest a new universal approach to study complex systems by microscopic, mesoscopic and macroscopic methods. We discuss new possibilities of extracting information on nonstationarity, unsteadiness and non-Markovity of discrete stochastic processes in complex systems. We consider statistical properties of the fast, intermediate and slow components of the investigated processes in complex systems within the framework of microscopic, mesoscopic and macroscopic approaches separately. Among them theoretical analysis is carried out by means of local noisy time-dependent parameters and the conception of a quasi-Brownian particle (QBP) (mesoscopic approach) as well as the use of wavelet transformation of the initial row time series. As a concrete example we examine the seismic time series data for strong and weak earthquakes in Turkey ($1998,1999$) in detail, as well as technogenic explosions. We propose a new way of possible solution to the problem of forecasting strong earthquakes forecasting. Besides we have found out that an unexpected restoration of the first two local noisy parameters in weak earthquakes and technogenic explosions is determined by exponential law. In this paper we have also carried out the comparison and have discussed the received time dependence of the local parameters for various seismic phenomena

Entanglement and Disentanglement in Circuit QED Architectures

We propose a protocol for creating entanglement within a dissipative circuit QED network architecture that consists of two electromagnetic circuits (cavities) and two superconducting qubits. The system interacts with a quantum environment, giving rise to decoherence and dissipation. We discuss the preparation of two separate entangled cavity-qubit states via Landau-Zener sweeps, after which the cavities interact via a tunable "quantum switch" which is realized with an ancilla qubit. Moreover, we discuss the decay of the resulting entangled two-cavity state due to the influence of the environment, where we focus on the entanglement decay.Comment: 7 pages, 5 figure

Interplay of frequency-synchronization with noise: current resonances, giant diffusion and diffusion-crests

We elucidate how the presence of noise may significantly interact with the synchronization mechanism of systems exhibiting frequency-locking. The response of these systems exhibits a rich variety of behaviors, such as resonances and anti-resonances which can be controlled by the intensity of noise. The transition between different locked regimes provokes the development of a multiple enhancement of the effective diffusion. This diffusion behavior is accompanied by a crest-like peak-splitting cascade when the distribution of the lockings is self-similar, as it occurs in periodic systems that are able to exhibit a Devil's staircase sequence of frequency-lockings.Comment: 7 pages, 6 figures, epl.cls. Accepted for publication in Europhysics Letter

Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation

The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy point-like Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, non-relativistic LE is deduced from this model, by taking into account the non-relativistic conservation laws for momentum and kinetic energy. Subsequently, this procedure is generalized to the relativistic case. There, it is found that the relativistic stochastic force is still \gd-correlated (white noise) but does \emph{no} longer correspond to a Gaussian white noise process. Explicit results for the friction and momentum-space diffusion coefficients are presented and discussed.Comment: v2: Eqs. (17c) and (28) corrected; v3: discussion extended, Eqs. (33) added, thereby connection to earlier work clarified; v4: final version, accepted for publication in Phys. Rev.

Coherence stabilization of a two-qubit gate by AC fields

We consider a CNOT gate operation under the influence of quantum bit-flip noise and demonstrate that ac fields can change bit-flip noise into phase noise and thereby improve coherence up to several orders of magnitude while the gate operation time remains unchanged. Within a high-frequency approximation, both purity and fidelity of the gate operation are studied analytically. The numerical treatment with a Bloch-Redfield master equation confirms the analytical results.Comment: 4 pages, 2 figure