Dephasing by a nonstationary classical intermittent noise

We consider a new phenomenological model for a $1/f^{\mu}$ classical intermittent noise and study its effects on the dephasing of a two-level system. Within this model, the evolution of the relative phase between the $|\pm>$ states is described as a continuous time random walk (CTRW). Using renewal theory, we find exact expressions for the dephasing factor and identify the physically relevant various regimes in terms of the coupling to the noise. In particular, we point out the consequences of the non-stationarity and pronounced non-Gaussian features of this noise, including some new anomalous and aging dephasing scenarii.Comment: Submitted to Phys. Rev.

Motional Broadening in Ensembles With Heavy-Tail Frequency Distribution

We show that the spectrum of an ensemble of two-level systems can be broadened through `resetting' discrete fluctuations, in contrast to the well-known motional-narrowing effect. We establish that the condition for the onset of motional broadening is that the ensemble frequency distribution has heavy tails with a diverging first moment. We find that the asymptotic motional-broadened lineshape is a Lorentzian, and derive an expression for its width. We explain why motional broadening persists up to some fluctuation rate, even when there is a physical upper cutoff to the frequency distribution.Comment: 6 pages, 4 figure

Lieb-Thirring Bound for Schr\"odinger Operators with Bernstein Functions of the Laplacian

A Lieb-Thirring bound for Schr\"odinger operators with Bernstein functions of the Laplacian is shown by functional integration techniques. Several specific cases are discussed in detail.Comment: We revised the first versio

Bardeen-Petterson effect and the disk structure of the Seyfert galaxy NGC 1068

VLBA high spatial resolution observations of the disk structure of the active galactic nucleus NGC 1068 has recently revealed that the kinematics and geometry of this AGN is well characterized by an outer disk of H2O maser emission having a compact milliarcsecond (parsec) scale structure, which is encircling a thin rotating inner disk surrounding a ~10^7 M_\sun compact mass, likely a black hole. A curious feature in this source is the occurrence of a misalignment between the inner and outer parts of the disk, with the galaxy's radio jet being orthogonal to the inner disk. We interpret this peculiar configuration as due to the Bardeen-Petterson effect, a general relativistic effect that warps an initially inclined (to the black hole equator) viscous disk, and drives the angular momentum vector of its inner part into alignment with the rotating black hole spin. We estimate the time-scale for both angular momenta to get aligned as a function the spin parameter of the Kerr black hole. We also reproduce the shape of the parsec and kiloparsec scale jets, assuming a model in which the jet is precessing with a period and aperture angle that decrease exponentially with time, as expected from the Bardeen-Petterson effect.Comment: 12 pages, 3 figures, accepted for publication in The Astrophysical Journa

Generalised extreme value statistics and sum of correlated variables

We show that generalised extreme value statistics -the statistics of the k-th largest value among a large set of random variables- can be mapped onto a problem of random sums. This allows us to identify classes of non-identical and (generally) correlated random variables with a sum distributed according to one of the three (k-dependent) asymptotic distributions of extreme value statistics, namely the Gumbel, Frechet and Weibull distributions. These classes, as well as the limit distributions, are naturally extended to real values of k, thus providing a clear interpretation to the onset of Gumbel distributions with non-integer index k in the statistics of global observables. This is one of the very few known generalisations of the central limit theorem to non-independent random variables. Finally, in the context of a simple physical model, we relate the index k to the ratio of the correlation length to the system size, which remains finite in strongly correlated systems.Comment: To appear in J.Phys.

Stationary states for underdamped anharmonic oscillators driven by Cauchy noise

Using methods of stochastic dynamics, we have studied stationary states in the underdamped anharmonic stochastic oscillators driven by Cauchy noise. Shape of stationary states depend both on the potential type and the damping. If the damping is strong enough, for potential wells which in the overdamped regime produce multimodal stationary states, stationary states in the underdamped regime can be multimodal with the same number of modes like in the overdamped regime. For the parabolic potential, the stationary density is always unimodal and it is given by the two dimensional $\alpha$-stable density. For the mixture of quartic and parabolic single-well potentials the stationary density can be bimodal. Nevertheless, the parabolic addition, which is strong enough, can destroy bimodlity of the stationary state.Comment: 9 page

On the relation between event-based and time-based current statistics

Current statistics can be calculated in various ways. Event-based approaches use the statistics of the number of events occuring during a given time. Time-based approaches use the statistics of the time needed to reach a given number of events. By analyzing normal as well as anomalous statistics of nonequilibrium currents through a two level system in contact with two different reservoirs, we investigate the conditions under which these different statistics do or do not yield identical predictions. We rely on the continuous time random walk formulation introduced in our earlier work [Phys. Rev. E 77, 051119 (2008)].Comment: 4 pages, 1 figure; v2: accepted in EPL 89, 10008 (2010

Exact and explicit probability densities for one-sided Levy stable distributions

We study functions g_{\alpha}(x) which are one-sided, heavy-tailed Levy stable probability distributions of index \alpha, 0< \alpha <1, of fundamental importance in random systems, for anomalous diffusion and fractional kinetics. We furnish exact and explicit expression for g_{\alpha}(x), 0 \leq x < \infty, satisfying \int_{0}^{\infty} exp(-p x) g_{\alpha}(x) dx = exp(-p^{\alpha}), p>0, for all \alpha = l/k < 1, with k and l positive integers. We reproduce all the known results given by k\leq 4 and present many new exact solutions for k > 4, all expressed in terms of known functions. This will allow a 'fine-tuning' of \alpha in order to adapt g_{\alpha}(x) to a given experimental situation.Comment: 4 pages, 3 figures and 1 tabl

Steady-State L\'evy Flights in a Confined Domain

We derive the generalized Fokker-Planck equation associated with a Langevin equation driven by arbitrary additive white noise. We apply our result to study the distribution of symmetric and asymmetric L\'{e}vy flights in an infinitely deep potential well. The fractional Fokker-Planck equation for L\'{e}vy flights is derived and solved analytically in the steady state. It is shown that L\'{e}vy flights are distributed according to the beta distribution, whose probability density becomes singular at the boundaries of the well. The origin of the preferred concentration of flying objects near the boundaries in nonequilibrium systems is clarified.Comment: 10 pages, 1 figur

Magnetically Torqued Thin Accretion Disks

We compute the properties of a geometrically thin, steady accretion disk surrounding a central rotating, magnetized star. The magnetosphere is assumed to entrain the disk over a wide range of radii. The model is simplified in that we adopt two (alternate) ad hoc, but plausible, expressions for the azimuthal component of the magnetic field as a function of radial distance. We find a solution for the angular velocity profile tending to corotation close to the central star, and smoothly matching a Keplerian curve at a radius where the viscous stress vanishes. The value of this ''transition'' radius is nearly the same for both of our adopted B-field models. We then solve analytically for the torques on the central star and for the disk luminosity due to gravity and magnetic torques. When expressed in a dimensionless form, the resulting quantities depend on one parameter alone, the ratio of the transition radius to the corotation radius. For rapid rotators, the accretion disk may be powered mostly by spin-down of the central star. These results are independent of the viscosity prescription in the disk. We also solve for the disk structure for the special case of an optically thick alpha disk. Our results are applicable to a range of astrophysical systems including accreting neutron stars, intermediate polar cataclysmic variables, and T Tauri systems.Comment: 9 sharper figs, updated reference