Nonstationary stochastic resonance viewed through the lens of information theory

In biological systems, information is frequently transferred with Poisson like spike processes (shot noise) modulated in time by information-carrying signals. How then to quantify information transfer for the output for such nonstationary input signals of finite duration? Is there some minimal length of the input signal duration versus its strength? Can such signals be better detected when immersed in noise stemming from the surroundings by increasing the stochastic intensity? These are some basic questions which we attempt to address within an analytical theory based on the Kullback-Leibler information concept applied to random processes

Theory of non-Markovian Stochastic Resonance

We consider a two-state model of non-Markovian stochastic resonance (SR) within the framework of the theory of renewal processes. Residence time intervals are assumed to be mutually independent and characterized by some arbitrary non-exponential residence time distributions which are modulated in time by an externally applied signal. Making use of a stochastic path integral approach we obtain general integral equations governing the evolution of conditional probabilities in the presence of an input signal. These novel equations generalize earlier integral renewal equations by Cox and others to the case of driving-induced non-stationarity. On the basis of these new equations a response theory of two state renewal processes is formulated beyond the linear response approximation. Moreover, a general expression for the linear response function is derived. The connection of the developed approach with the phenomenological theory of linear response for manifest non-Markovian SR put forward in [ I. Goychuk and P. Hanggi, Phys. Rev. Lett. 91, 070601 (2003)] is clarified and its range of validity is scrutinized. The novel theory is then applied to SR in symmetric non-Markovian systems and to the class of single ion channels possessing a fractal kinetics

The Tasaki-Crooks quantum fluctuation theorem

Starting out from the recently established quantum correlation function expression of the characteristic function for the work performed by a force protocol on the system [cond-mat/0703213] the quantum version of the Crooks fluctuation theorem is shown to emerge almost immediately by the mere application of an inverse Fourier transformation

Transport of overdamped Brownian particles in a two-dimensional tube: Nonadiabatic regime

Transport of overdamped Brownian particles in a two-dimensional asymmetric tube is investigated in the presence of nonadiabatic periodic driving forces. By using Brownian dynamics simulations we can find that the phenomena in nonadiabatic regime differ from that in adiabatic case. The direction of the current can be reversed by tuning the driving frequency. Remarkably, the current as a function of the driving amplitude exhibits several local maxima at finite driving frequency.Comment: 10 pages, 4 figure

Electronic Heat Transport Across a Molecular Wire: Power Spectrum of Heat Fluctuations

With this study we analyze the fluctuations of an electronic only heat current across a molecular wire. The wire is composed of a single energy level which connects to two leads which are held at different temperatures. By use of the Green function method we derive the finite frequency power spectral density (PSD) of the emerging heat current fluctuations. This result assumes a form quite distinct from the power spectral density of the accompanying electric current noise. The complex expression simplifies considerably in the limit of zero frequency, yielding the heat noise intensity. The heat noise intensity still depends on the frequency in the zero-temperature limit, assuming different asymptotic behaviors in the low- and high-frequency regimes. These findings evidence that heat transport across molecular junctions can exhibit a rich structure beyond the common behavior which emerges in the linear response limit

In-phase and anti-phase synchronization in noisy Hodgkin-Huxley neurons

We numerically investigate the influence of intrinsic channel noise on the dynamical response of delay-coupling in neuronal systems. The stochastic dynamics of the spiking is modeled within a stochastic modification of the standard Hodgkin-Huxley model wherein the delay-coupling accounts for the finite propagation time of an action potential along the neuronal axon. We quantify this delay-coupling of the Pyragas-type in terms of the difference between corresponding presynaptic and postsynaptic membrane potentials. For an elementary neuronal network consisting of two coupled neurons we detect characteristic stochastic synchronization patterns which exhibit multiple phase-flip bifurcations: The phase-flip bifurcations occur in form of alternate transitions from an in-phase spiking activity towards an anti-phase spiking activity. Interestingly, these phase-flips remain robust in strong channel noise and in turn cause a striking stabilization of the spiking frequency

Driven Tunneling: Chaos and Decoherence

Chaotic tunneling in a driven double-well system is investigated in absence as well as in the presence of dissipation. As the constitutive mechanism of chaos-assisted tunneling, we focus on the dynamics in the vicinity of three-level crossings in the quasienergy spectrum. The coherent quantum dynamics near the crossing is described satisfactorily by a three-state model. It fails, however, for the corresponding dissipative dynamics, because incoherent transitions due to the interaction with the environment indirectly couple the three states in the crossing to the remaining quasienergy states. The asymptotic state of the driven dissipative quantum dynamics partially resembles the, possibly strange, attractor of the corresponding damped driven classical dynamics, but also exhibits characteristic quantum effects.Comment: 32 pages, 35 figures, lamuphys.st

Entanglement creation in circuit QED via Landau-Zener sweeps

A qubit may undergo Landau-Zener transitions due to its coupling to one or several quantum harmonic oscillators. We show that for a qubit coupled to one oscillator, Landau-Zener transitions can be used for single-photon generation and for the controllable creation of qubit-oscillator entanglement, with state-of-the-art circuit QED as a promising realization. Moreover, for a qubit coupled to two cavities, we show that Landau-Zener sweeps of the qubit are well suited for the robust creation of entangled cavity states, in particular symmetric Bell states, with the qubit acting as the entanglement mediator. At the heart of our proposals lies the calculation of the exact Landau-Zener transition probability for the qubit, by summing all orders of the corresponding series in time-dependent perturbation theory. This transition probability emerges to be independent of the oscillator frequencies, both inside and outside the regime where a rotating-wave approximation is valid.Comment: 12 pages, 7 figure