Search results for "Periodic function"

Quantum walk with a time-dependent coin

2006

We introduce quantum walks with a time-dependent coin, and show how they include, as a particular case, the generalized quantum walk recently studied by Wojcik et al. {[}Phys. Rev. Lett. \textbf{93}, 180601(2004){]} which exhibits interesting dynamical localization and quasiperiodic dynamics. Our proposal allows for a much easier implementation of this particular rich dynamics than the original one. Moreover, it allows for an additional control on the walk, which can be used to compensate for phases appearing due to external interactions. To illustrate its feasibility, we discuss an example using an optical cavity. We also derive an approximated solution in the continuous limit (long--wavel…

Unitary time-dependent superconvergent technique for pulse-driven quantum dynamics

2003

We present a superconvergent Kolmogorov-Arnold-Moser type of perturbation theory for time-dependent Hamiltonians. It is strictly unitary upon truncation at an arbitrary order and not restricted to periodic or quasiperiodic Hamiltonians. Moreover, for pulse-driven systems we construct explicitly the KAM transformations involved in the iterative procedure. The technique is illustrated on a two-level model perturbed by a pulsed interaction for which we obtain convergence all the way from the sudden regime to the opposite adiabatic regime.

Imprints of superfluidity on magnetoelastic quasiperiodic oscillations of soft gamma-ray repeaters.

2013

Our numerical simulations show that axisymmetric, torsional, magnetoelastic oscillations of magnetars with a superfluid core can explain the whole range of observed quasiperiodic oscillations (QPOs) in the giant flares of soft gamma-ray repeaters. There exist constant phase QPOs at $f\ensuremath{\lesssim}150\text{ }\text{ }\mathrm{Hz}$ and resonantly excited high-frequency QPOs ($fg500\text{ }\text{ }\mathrm{Hz}$), in good agreement with observations. The range of magnetic field strengths required to match the observed QPO frequencies agrees with that from spin-down estimates. These results suggest that there is at least one superfluid species in magnetar cores.

Chaotic Antiferromagnetic Nano-Oscillator driven by Spin-Torque

2021

We theoretically describe the behavior of a terahertz nano-oscillator based on an anisotropic antiferromagnetic dynamical element driven by spin torque. We consider the situation when the polarization of the spin-current is perpendicular to the external magnetic field applied along the anisotropy easy-axis. We determine the domain of the parametric space (field, current) where the oscillator demonstrates chaotic dynamics. Characteristics of the chaotic regimes are analyzed using conventional techniques such as spectra of the Lyapunov exponents. We show that the threshold current of the chaos appearance is particularly low in the vicinity of the spin-flop transition. In this regime, we consi…

Nonlinear parametric resonances in quasiperiodic dispersion oscillating fibers

2015

We numerically study the evolution of the spectrum of parametric resonance or modulation instability sidebands in quasiperiodic dispersion oscillating fibers. We separately consider a linear variation along the fiber of either the spatial period, the average dispersion, or the amplitude of the dispersion oscillation. We found that this linear variation of the dispersion oscillating fiber parameters may provide different novel mechanisms for the splitting of the resonance sideband spectrum, owing to coherent interference between quasi-resonant waves that are generated at different points along the fiber. (C) 2015 Elsevier B.V. All rights reserved.

The bistable potential: An archetype for classical and quantum systems

2012

In this work we analyze the transient dynamics of three different classical and quantum systems. First, we consider a classical Brownian particle moving in an asymmetric bistable potential, subject to a multiplicative and additive noise source. We investigate the role of these two noise sources on the life time of the metastable state. A nonmonotonic behavior of the lifetime as a function of both additive and multiplicative noise intensities is found, revealing the phenomenon of noise enhanced stability. Afterward, by using a LotkaVolterra model, the dynamics of two competing species in the presence of Lévy noise sources is analyzed. Quasiperiodic oscillations and stochastic resonance pheno…

Identification of spatially confined states in two-dimensional quasiperiodic lattices.

1995

We study the electronic eigenstates on several two-dimensional quasiperiodic lattices, such as the Penrose lattice and random-tiling lattices, using a tight-binding Hamiltonian in the vertex model. The infinitely degenerate states at E=0 are especially investigated. We present a systematic procedure which allows us to identify numerically the spatially strongly localized so-called confined states.

Intermittent and quasiperiodic behavior in a Zeeman laser model with large cavity anisotropy

1997

Local Asymptotic Normality for Shape and Periodicity in the Drift of a Time Inhomogeneous Diffusion

2017

We consider a one-dimensional diffusion whose drift contains a deterministic periodic signal with unknown periodicity $T$ and carrying some unknown $d$-dimensional shape parameter $\theta$. We prove Local Asymptotic Normality (LAN) jointly in $\theta$ and $T$ for the statistical experiment arising from continuous observation of this diffusion. The local scale turns out to be $n^{-1/2}$ for the shape parameter and $n^{-3/2}$ for the periodicity which generalizes known results about LAN when either $\theta$ or $T$ is assumed to be known.

Ergodicity and limit theorems for degenerate diffusions with time periodic drift. Application to a stochastic Hodgkin−Huxley model

2016

We formulate simple criteria for positive Harris recurrence of strongly degenerate stochastic differential equations with smooth coefficients on a state space with certain boundary conditions. The drift depends on time and space and is periodic in the time argument. There is no time dependence in the diffusion coefficient. Control systems play a key role, and we prove a new localized version of the support theorem. Beyond existence of some Lyapunov function, we only need one attainable inner point of full weak Hoermander dimension. Our motivation comes from a stochastic Hodgkin−Huxley model for a spiking neuron including its dendritic input. This input carries some deterministic periodic si…