Related papers: 1/f^beta noise in a model for weak ergodicity brea…
The power spectrum of quantum dot fluorescence exhibits $1/f^\beta$ noise, related to the intermittency of these nanosystems. As in other systems exhibiting $1/f$ noise, this power spectrum is not integrable at low frequencies, which…
The origin of the low-frequency noise with power spectrum $1/f^\beta$ (also known as $1/f$ fluctuations or flicker noise) remains a challenge. Recently, the nonlinear stochastic differential equations for modeling $1/f^\beta$ noise have…
We find a general formula for the distribution of time averaged observables for weakly non-ergodic systems. Such type of ergodicity breaking is known to describe certain systems which exhibit anomalous fluctuations, e.g. blinking quantum…
Power spectral density scaling with frequency $f$ as $1/f^\beta$ and $\beta \approx 1$ is widely found in natural and socio-economic systems. Consequently, it has been suggested that such self-similar spectra reflect the universal dynamics…
We study the power spectrum which is estimated from a nonstationary signal. In particular we examine the case when the signal is observed in a measurement time window $[t_w,t_w+t_m]$, namely the observation started after a waiting time…
Starting from the developed generalized point process model of $1/f$ noise (B. Kaulakys et al, Phys. Rev. E 71 (2005) 051105; cond-mat/0504025) we derive the nonlinear stochastic differential equations for the signal exhibiting 1/f^{\beta}$…
Noise of stochastic processes whose power spectrum scales at low frequencies, $f$, as $1/f$ appears in such diverse systems that it is considered universal. However, there have been a small number of instances from completely unrelated…
We analyze the power spectral density of a signal composed of nonoverlapping rectangular pulses. First, we derive a general formula for the power spectral density of a signal constructed from the sequence of nonoverlapping pulses. Then we…
Recent experiments on blinking quantum dots and weak turbulence in liquid crystals reveal the fundamental connection between $1/f$ noise and power law intermittency. The non-stationarity of the process implies that the power spectrum is…
We present a simple point process model of $1/f^{\beta}$ noise, covering different values of the exponent $\beta$. The signal of the model consists of pulses or events. The interpulse, interevent, interarrival, recurrence or waiting times…
Quantum chaotic and integrable systems are known to exhibit a characteristic $1/f$ and $1/f^{2}$ noise, respectively, in the power spectrum associated to their spectral fluctuations. A recent work [R. Riser, V. A. Osipov, and E. Kanzieper,…
One of the primitive aims of the two-dimensional BTW model had been to explain the $1/f^{\alpha}$ noise which is widely seen in the natural systems. In this paper we study some time signals, namely the activity inside an avalanche ($x(t)$),…
The power spectrum of a stationary process may be calculated in terms of the autocorrelation function using the Wiener-Khinchin theorem. We here generalize the Wiener-Khinchin theorem for nonstationary processes and introduce a…
The power law $1/f^{\alpha}$ in the power spectrum characterizes the fluctuating observables of many complex natural systems. Considering the energy levels of a quantum system as a discrete time series where the energy plays the role of…
We find a general formula for the distribution of time-averaged observables for systems modeled according to the sub-diffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and…
Simple analytically solvable models are proposed exhibiting 1/f spectrum in wide range of frequency. The signals of the models consist of pulses (point process) which interevent times fluctuate about some average value, obeying an…
We investigate the row sum of the binary pattern generated by the Sierpinski automaton: Interpreted as a time series we calculate the power spectrum of this Sierpinski signal analytically and obtain a unique rugged fine structure with…
We describe a non-perturbative method for computing the energy band structures of one-dimensional models with general point potentials sitting at equally spaced sites. This is done thanks to a Bethe ansatz approach and the method is…
It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the behavior of the power spectrum of the excitation energy fluctuations, which is…
The power density spectrum of a light curve is often calculated as the average of a number of spectra derived on individual time intervals the light curve is divided into. This procedure implicitly assumes that each time interval is a…