Signature of chaos in power spectrum

We investigate the nature of the numerically computed power spectral densityP(f, N, τ) of a discrete (sampling time interval,τ) and finite (length,N) scalar time series extracted from a continuous time chaotic dynamical system. We highlight howP(f, N, τ) differs from the true power spectrum and from the power spectrum of a general stochastic process. Non-zeroτ leads to aliasing;P(f, N, τ) decays at high frequencies as [πτ/sinπτf]², which is an aliased form of the 1/f ² decay. This power law tail seems to be a characteristic feature of all continuous time dynamical systems, chaotic or otherwise. Also the tail vanishes in the limit ofN → ∞, implying that the true power spectral density must be band width limited. In striking contrast the power spectrum of a stochastic process is dominated by a term independent of the length of the time series at all frequencies.     

The power of chaos

Numerical experiments performed with the Hénon-Heiles oscillator reveal that quasi-periodic and chaotic solutions of Hamiltonian systems can be differentiated on the basis of the structure of their power spectra. While we illustrate in this paper that mere visual inspection of the distribution of power already discloses striking differences between both classes of solution, we attempt to develop more objective structural criteria.It is found that the fractal dimension of the renormalised power spectrum lends itself to a convenient global characterisation of the geometry of the latter, capable, in principle, of discriminating between quasi-periodicity and chaos.     

Reconstruction of the surface power spectrum from reflectivity data

An analytical approach is used to determine the power spectrum of the surface roughness from experimental data for the reflectivity of randomly rough surfaces. A one-dimensional, randomly rough, perfectly conducting surface that is illuminated by s-polarized light whose plane of incidence is perpendicular to the generators of the surface is considered, and the power spectrum is obtained within the framework of phase perturbation theory. Good agreement with numerically generated experimental data is obtained.     

Random-phase-induced chaos in power systems

This paper studies how random phase (namely, noise-perturbed phase) effects the dynamical behaviours of a simple model of power system which operates in a stable regime far away from chaotic behaviour in the absence of noise. It finds that when the phase perturbation is weak, chaos is absent in power systems. With the increase of disturbed intensity $\sigma$, power systems become unstable and fall into chaos as $\sigma$ further increases. These phenomena imply that random phase can induce and enhance chaos in power systems. Furthermore, the possible mechanism behind the action of random phase is addressed.     

Measuring the tilt of primordial gravitational-wave power spectrum from observations

Size effect on thermodynamics and diffusion of deuterium in nano-sized vanadium(V) layers is studied. Critical temperature(Tc)for deuterium phase transition is found to decrease with the inverse thickness of V layers and the thermodynamic factor increases as V thickness decreases. These effects are related to the deuterium-deuterium(D-D) interaction change versus V thickness,which experimentally proves that the D-D interaction plays the main contribution to the previously observed V size effect on deuterium chemical diffusion coefficients(D_c). The self-diffusion coefficients(D_s) are obtained through correcting D_c with the thermodynamic factors. It is found that the D_s are similar in 14 and 28 monolayers of V while slightly larger D_s are observed at high concentrations in 14 atomic layers. The weak site blocking effect in the interface is argued to be the main contribution to the observed size effect on D_s.     

Doppler power spectrum from a Gaussian sample volume

A closed-form expression for the Doppler power spectrum due solely to the range of blood velocities passing through a Gaussian sample volume placed anywhere in a vessel under conditions of axisymmetric flow, uniform backscatter and negligible intrinsic spectral broadening has been derived. The formulation presented here allows the independent specification of the sample volume position and width, in the three dimensions, and enables simple estimations of spectral shape for pulsed wave Doppler systems. Simpler expressions were derived for the cases of symmetric sample volume projections onto the vessel cross-section and/or sample volumes centred in the vessel. Closed form expressions were derived for mean frequency and spectral width in the case of a symmetric sample volume projection centred in the vessel. The effects of sample volume size and position on the Doppler spectral width and mean frequency are shown for a range of velocity profiles.     

Primordial non-Gaussianity from the 21 cm power spectrum during the epoch of reionization

Primordial non-Gaussianity is a crucial test of inflationary cosmology. We consider the impact of non-Gaussianity on the ionization power spectrum from 21 cm emission at the epoch of reionization. We focus on the power spectrum on large scales at redshifts of 7 to 8 and explore the expected constraint on the local non-Gaussianity parameter f(NL) for current and next-generation 21 cm experiments. We show that experiments such as SKA and MWA could measure f(NL) values of order 10. This can be improved by an order of magnitude with a fast-Fourier transform telescope like Omniscope.     

The power spectrum of the circular noise

The circular noise is important in connection to Mach's principle, and also as a possible probe of the Unruh effect. In this letter the power spectrum of the detector following the Trocheries-Takeno motion in the Minkowski vacuum is analytically obtained in the form of an infinite series. A mean distribution function and corresponding energy density are obtained for this particular detected noise. The analogous of a non constant temperature distribution is obtained. And in the end, a brief discussion about the equilibrium configuration is given.     

Erratum to: Measuring the tilt of primordial gravitational-wave power spectrum from observations

Geometric phases are only dependent on evolution paths but independent of evolution details so that they possess some intrinsic noise-resilience features. Based on different geometric phases, various quantum gates have been proposed, such as nonadiabatic geometric gates based on nonadiabatic Abelian geometric phases and nonadiabatic holonomic gates based on nonadiabatic nonAbelian geometric phases. Up to now, nonadiabatic holonomic one-qubit gates have been experimentally demonstrated with superconducting transmons, where the three lowest levels are all utilized in operation. However, the second excited state of transmons has a relatively short coherence time, which results in a decreased fidelity of quantum gates. Here, we experimentally realize Abelian-geometric-phase-based nonadiabatic geometric one-qubit gates with a superconducting Xmon qubit. The realization is performed on the two lowest levels of an Xmon qubit and thus avoids the influence from the short coherence time of the second excited state. The experimental result indicates that the average fidelities of single-qubit gates can be up to 99.6% and 99.7% characterized by quantum process tomography and randomized benchmarking.     

由傅里叶功率谱恢复物函数的研究

相位恢复工作中,针对物函数是实函数的情形,Fienup算法取得了较大的成功.本文给出一新算法,其收敛程度比Fienup算法更优.以天文学中双星情形为例,比较了两种不同算法的结果.     

Controlling chaos in a satellite power supply subsystem

In this work, we show that chaos control techniques can be used to increase the region that can be efficiently used to supply the power requests for an artificial satellite. The core of a satellite power subsystem relies on its DC/DC converter. This is a very nonlinear system that presents a multitude of phenomena ranging from bifurcations, quasi-periodicity, chaos, coexistence of attractors, among others. The traditional power subsystem design techniques try to avoid these nonlinear phenomena so that it is possible to use linear system theory in small regions about the equilibrium points. Here, we show that chaos control can be used to efficiently extend the applicability region of the satellite power subsystem when it operates in regions of high nonlinearity.     

Exponential decay of the power spectrum of turbulence

The analyticity on a strip of the solutions of Navier-Stokes equations in 2D is shown to explain the observed fast decay of the frequency power spectrum of the turbulent velocity field. Some subtleties in the application of the Wiener-Khinchine method to turbulence are resolved by showing that the frequency power spectrum of turbulent velocities is in fact a measure exponentially decaying for frequency ±. Our approach also shows that the conventional procedures used in analyzing data in turbulence experiments are valid even in the absence of the ergodic property in the flow.     

反馈强度调制增强混沌光通信的保密性

注入锁定式光混沌同步通信系统对收发机的参数失配有较大的容忍度,这在一定程度上降低了信息的安全性.提出采用反馈强度的调制来提高系统的保密性.数值模拟分析了调制前后系统提取信号质量的变化,以及收发机调制的速率失谐、延时对提取信号质量的影响.研究发现：仅在发射机增加反馈强度调制后,同步性恶化、误码率增大两个数量级,无法提取信号;而在接收机引入相同的调制后,系统同步性及误码率得到恢复.此外,收发机的反馈强度调制速率失谐和延时范围分别在±5 MHz和±0.1倍调制周期时,信息提取质量较高.反馈强度调制能够有效地增强传统混沌通信系统的保密性. 关键词： 反馈强度 调制 混沌通信 保密     

A statistical analysis of hadron spectrum: Quantum chaos in hadrons

The nearest-neighbor mass-spacing distribution of the meson and baryon spectrum (up to 2.5 GeV) is described by the Wigner surmise corresponding to the statistics of the Gaussian orthogonal ensemble of random matrix theory. This can be viewed as a manifestation of quantum chaos in hadrons. Received: 30 September 2002 / Accepted: 21 November 2002 / Published online: 4 February 2003 RID="a" ID="a"Present address: Department of Physics and Astronomy, Ohio University, Athens, OH 45701, USA; e-mail: vlad@phy.ohiou.edu Communicated by G. Orlandini