Fractional time random walk subdiffusion and anomalous transport with finite mean residence times: faster, not slower

Continuous time random walk (CTRW) subdiffusion along with the associated fractional Fokker-Planck equation (FFPE) is traditionally based on the premise of random clock with divergent mean period. This work considers an alternative CTRW and FFPE description which is featured by finite mean residence times (MRTs) in any spatial domain of finite size. Transient subdiffusive transport can occur on a very large time scale $\tau_c$ which can greatly exceed mean residence time in any trap, $\tau_c\gg$, and even not being related to it. Asymptotically, on a macroscale transport becomes normal for $t\gg\tau_c$. However, mesoscopic transport is anomalous. Differently from viscoelastic subdiffusion no long-range anti-correlations among position increments are required. Moreover, our study makes it obvious that the transient subdiffusion and transport are faster than one expects from their normal asymptotic limit on a macroscale. This observation has profound implications for anomalous mesoscopic transport processes in biological cells because of macroscopic viscosity of cytoplasm is finite

Driven Tunneling Dynamics: Bloch-Redfield Theory versus Path Integral Approach

In the regime of weak bath coupling and low temperature we demonstrate numerically for the spin-boson dynamics the equivalence between two widely used but seemingly different roads of approximation, namely the path integral approach and the Bloch-Redfield theory. The excellent agreement between these two methods is corroborated by a novel efficient analytical high-frequency approach: it well approximates the decay of quantum coherence via a series of damped coherent oscillations. Moreover, a suitably tuned control field can selectively enhance or suppress quantum coherence.Comment: 4 pages including 3 figures, submitted for publicatio

Mandelbrot's 1/f fractional renewal models of 1963-67: The non-ergodic missing link between change points and long range dependence

The problem of 1/f noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot's fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal models, I present preliminary results of my research into the history of Mandelbrot's very little known work in that area from 1963-67. I speculate about how the lack of awareness of this work in the physics and statistics communities may have affected the development of complexity science, and I discuss the differences between the Hurst effect, 1/f noise and LRD, concepts which are often treated as equivalent.Comment: 11 pages. Corrected and improved version of a manuscript submitted to ITISE 2016 meeting in Granada, Spai

Controlling decoherence of a two-level-atom in a lossy cavity

By use of external periodic driving sources, we demonstrate the possibility of controlling the coherent as well as the decoherent dynamics of a two-level atom placed in a lossy cavity. The control of the coherent dynamics is elucidated for the phenomenon of coherent destruction of tunneling (CDT), i.e., the coherent dynamics of a driven two-level atom in a quantum superposition state can be brought practically to a complete standstill. We study this phenomenon for different initial preparations of the two-level atom. We then proceed to investigate the decoherence originating from the interaction of the two-level atom with a lossy cavity mode. The loss mechanism is described in terms of a microscopic model that couples the cavity mode to a bath of harmonic field modes. A suitably tuned external cw-laser field applied to the two-level atom slows down considerably the decoherence of the atom. We demonstrate the suppression of decoherence for two opposite initial preparations of the atomic state: a quantum superposition state as well as the ground state. These findings can be used to the effect of a proficient battling of decoherence in qubit manipulation processes.Comment: 12 pages including 3 figures, submitted for publicatio

Driving-Induced Symmetry Breaking in the Spin-Boson System

A symmetric dissipative two-state system is asymptotically completely delocalized independent of the initial state. We show that driving-induced localization at long times can take place when both the bias and tunneling coupling energy are harmonically modulated. Dynamical symmetry breaking on average occurs when the driving frequencies are odd multiples of some reference frequency. This effect is universal, as it is independent of the dissipative mechanism. Possible candidates for an experimental observation are flux tunneling in the variable barrier rf SQUID and magnetization tunneling in magnetic molecular clusters.Comment: 4 pages, 4 figures, to be published in PR

Quantum dynamics in strong fluctuating fields

A large number of multifaceted quantum transport processes in molecular systems and physical nanosystems 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. Herein, 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 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.Comment: review article, Advances in Physics (2005), in pres

Two coupled Josephson junctions: dc voltage controlled by biharmonic current

We study transport properties of two Josephson junctions coupled by an external shunt resistance. One of the junction (say, the first) is driven by an unbiased ac current consisting of two harmonics. The device can rectify the ac current yielding a dc voltage across the first junction. For some values of coupling strength, controlled by an external shunt resistance, a dc voltage across the second junction can be generated. By variation of system parameters like the relative phase or frequency of two harmonics, one can conveniently manipulate both voltages with high efficiency, e.g., changing the dc voltages across the first and second junctions from positive to negative values and vice versa.Comment: 15 pages, 7 figures, to appear in J. Phys. Condens. Matter (2012

Directed current due to broken time-space symmetry

We consider the classical dynamics of a particle in a one-dimensional space-periodic potential U(X) = U(X+2\pi) under the influence of a time-periodic space-homogeneous external field E(t)=E(t+T). If E(t) is neither symmetric function of t nor antisymmetric under time shifts $E(t \pm T/2) \neq -E(t)$, an ensemble of trajectories with zero current at t=0 yields a nonzero finite current as $t\to \infty$. We explain this effect using symmetry considerations and perturbation theory. Finally we add dissipation (friction) and demonstrate that the resulting set of attractors keeps the broken symmetry property in the basins of attraction and leads to directed currents as well.Comment: 2 figure

Stochastic resonance as a collective property of ion channel assemblies

By use of a stochastic generalization of the Hodgkin-Huxley model we investigate both the phenomena of stochastic resonance (SR) and coherence resonance (CR) in variable size patches of an excitable cell membrane. Our focus is on the challenge how internal noise stemming from individual ion channels does affect collective properties of the whole ensemble. We investigate both an unperturbed situation with no applied stimuli and one in which the membrane is stimulated externally by a periodic signal and additional external noise. For the nondriven case, we demonstrate the existence of an optimal size of the membrane patch for which the internal noise causes a most regular spike activity. This phenomenon shall be termed intrinsic CR. In presence of an applied periodic stimulus we demonstrate that the signal-to-noise ratio (SNR) exhibits SR vs. decreasing patch size, or vs. increasing internal noise strength, respectively. Moreover, we demonstrate that conventional SR vs. the external noise intensity occurs only for sufficiently large membrane patches, when the intensity of internal noise is below its optimal level. Thus, biological SR seemingly is rooted in the collective properties of large ion channel ensembles rather than in the individual stochastic dynamics of single ion channels.Comment: 9 pages, 2 figure