Papers by Bronius Kaulakys
Jetp Letters, Jul 1, 1979
It is shown that resonance scattering introduces an important contribution to the broadening and ... more It is shown that resonance scattering introduces an important contribution to the broadening and displacement of the Rydberg series in atoms and explains the presence of oscillations. Analysis of the experimental data permits the reconstruction of the binding energy of the quasidiscrete level for a negative ion, its autoionization width, orbital angular momentum, and its multiplicity.
We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained
Institute of Theoretical Physics and Astronomy, Vilnius University,A. Goˇstauto 12, LT-01108 Viln... more Institute of Theoretical Physics and Astronomy, Vilnius University,A. Goˇstauto 12, LT-01108 Vilnius, Lithuania(Dated: February 23, 2010)We consider a class of nonlinear stochastic differential equations, giving the power-law behavior ofthe power spectral density in any desirably wide range of frequency. Such equations were obtainedstarting from the point process models of 1/f
We investigate a transition from chaotic to nonchaotic behavior and synchronization in an ensembl... more We investigate a transition from chaotic to nonchaotic behavior and synchronization in an ensemble of systems driven by identical random forces. We analyze the synchronization phenomenon in the ensemble of particles moving with friction in the time-dependent potential and driven by the identical noise. We define the threshold values of the parameters for transition from chaotic to nonchaotic behavior and investigate dependencies of the Lyapunov exponents and power spectral density on the nonlinearity of the systems and character of the driven force.
Eprint Arxiv Quant Ph 9610019, Oct 1, 1996
The effect of repetitive measurement for quantum dynamics of driven by an intensive external forc... more The effect of repetitive measurement for quantum dynamics of driven by an intensive external force of the simple few-level systems as well as of the multilevel systems that exhibit the quantum localisation of classical chaos is investigated. Frequent measurement of the simple system yields to the quantum Zeno effect while that of the suppressed quantum system, which classical counterpart exhibits chaos, results in the delocalisation of the quantum suppression. From the analysis we may conclude that continuously observable quasiclassical system evolves essentially classically-like.
Eprint Arxiv Quant Ph 9610041, Oct 1, 1996
A simple theory of the Rydberg atoms ionisation by electromagnetic pulses and microwave field is ... more A simple theory of the Rydberg atoms ionisation by electromagnetic pulses and microwave field is presented. The analysis is based on the scale transformation which reduces the number of parameters and reveals the functional dependencies of the processes. It is shown that the observed ionisation of Rydberg atoms by subpicosecond electromagnetic pulses scale classically. The threshold electric field required to
AIP Conference Proceedings, 1995
A simple theory of the Rydberg atoms ionisation by electromagnetic pulses and microwave field is ... more A simple theory of the Rydberg atoms ionisation by electromagnetic pulses and microwave field is presented. The analysis is based on the scale transformation which reduces the number of parameters and reveals the functional dependencies of the processes. It is shown that the observed ionisation of Rydberg atoms by subpicosecond electromagnetic pulses scale classically. The threshold electric field required to ionise a Rydberg state may be simply evaluated in the photonic basis approach for the quantum dynamics or from the multiphoton ionisation theory.
Evolution of Complex Systems and 1/f Noise: from Physics to Financial Markets
Solid State Phenomena, 2004
We introduce the stochastic multiplicative model of time intervals between the events, defining a... more We introduce the stochastic multiplicative model of time intervals between the events, defining a multiplicative point process and analyze the statistical properties of the signal. Such a model system exhibits power-law spectral density S(f)~1/fβ, scaled as power of frequency for various values of β between 0.5 and 2. We derive explicit expressions for the power spectrum and other statistics and analyze the model system numerically. The specific interest of our analysis is related with the theoretical modeling of the nonlinear complex systems exhibiting fractal behavior and self-organization.
We investigate a problem of the necessary and sufficient conditions for appearance of the 1/f flu... more We investigate a problem of the necessary and sufficient conditions for appearance of the 1/f fluctuations in the simple systems affected by the external random perturbations, i.e. the power spectral density of the flux of particles moving in some contours and perturbed by the external forces. In some cases we observe the 1/f behavior but only in some range of
Journal of Physics B: Atomic and Molecular Physics, 1987
The non-stationary multistep (diffusion-like) ionisation of Rydberg atoms is considered theoretic... more The non-stationary multistep (diffusion-like) ionisation of Rydberg atoms is considered theoretically. The investigation is based on the time-dependent Fokker-Planck equation and is related to collisional and microwave ionisation of Rydberg atoms. Analytical expressions for the mean time and the higher moments of the distribution of the diffusive ionisation times are derived. The conditions for the occurrence of diffusive ionisation are obtained. The relation of the present study to stationary diffusive ionisation and the experimental investigation of the ionisation of Rydberg atoms is discussed.
Physical Review E, 1995
A theoretical and numerical analysis of the transition from chaotic to nonchaotic behavior in an ... more A theoretical and numerical analysis of the transition from chaotic to nonchaotic behavior in an ensemble of particles with different initial conditions which move according to Newton's equations in a bounding potential and are driven by an identical sequence of random forces (see S. Fahy and D. R. Hamann, Phys. Rev. Lett. 69, 761 (1992)) is presented. The threshold values of the parameters for transition from chaotic to nonchaotic behavior are defined on the basis of the map for distances between the particles and differences of velocity. Numerical analysis is fulfilled for one-dimensional Duffing V (x) = x 4 -x 2 and V (x) = x 4 potentials. PACS number(s): 05.40.+j, 05.45.+b Recently an interesting transition from chaotic to nonchaotic behavior in randomly driven systems has been discovered [1]. When an ensemble of bounded in a fixed external potential particles with different initial conditions
Journal of Statistical Mechanics: Theory and Experiment, 2014
There are several mathematical models yielding 1/f noise. For example, 1/f spectrum can be obtain... more There are several mathematical models yielding 1/f noise. For example, 1/f spectrum can be obtained from stochastic sequence of pulses having power-law distribution of pulse durations or from nonlinear stochastic differential equations. We show that a couple of seemingly different models exhibiting 1/f spectrum are due to the similar scaling properties of the signals. In addition, we demonstrate a connection between signals with the power-law behavior of the power spectral density generated by the nonlinear stochastic differential equations and modeled by a sequence of random different pulses. An approximation of solutions of the nonlinear stochastic differential equations by the sequence of pulses correctly reproduces the power-law parts of the probability density function and of the power spectral density. This connection provides further insights into the origin of 1/f noise.
Intermittency generating 1/f noise
2013 22nd International Conference on Noise and Fluctuations (ICNF), 2013
ABSTRACT We analyze a mechanism of intermittency in nonlinear dynamical systems having the invari... more ABSTRACT We analyze a mechanism of intermittency in nonlinear dynamical systems having the invariant subspace and zero transverse Lyapunov exponent. Our model is similar to the on-off intermittency, occurring due the time-dependent forcing of a bifurcation parameter through a bifurcation point but with nonzero transverse Lyapunov exponent. We show that our nonlinear dynamical systems exhibit 1/fβ noise of the deviation from the invariant subspace. Further, the approximation of the intermittency generating maps by the nonlinear stochastic differential equations is presented and the connection with the equations modeling 1/fβ noise is established.
Solution of the Equations of Dynamical Chaos
Proceedings of the Second International Conference in Honour of J. Kubilius, Palanga, Lithuania, 23-27 September 1996
Complexus Mundi, 2006
Multiplicative processes and multifractals have earned increased popularity in applications rangi... more Multiplicative processes and multifractals have earned increased popularity in applications ranging from hydrodynamic turbulence to computer network traffic, from image processing to economics. We analyse the multifractality of the recently proposed point process models generating the signals exhibiting 1/f β noise. The models may be used for modeling and analysis of stochastic processes in different systems. We show that the multiplicative point process models generate multifractal signals, in contrast to the formally constructed signals with 1/f β noise and signals consisting of sum of the uncorrelated components with a wide-range distribution of the relaxation times.
Traffic and Granular Flow ' 05, 2007
We present analytical and numerical results of modeling of flows represented as the correlated no... more We present analytical and numerical results of modeling of flows represented as the correlated non-Poissonian point process and as the Poissonian sequence of pulses of the different size. Both models may generate signals with the powerlaw distributions of the intensity of the flow and the power-law spectral density. Furthermore, different distributions of the interevent time of the point process and different statistics of the size of pulses may result in 1/f β noise with 0.5 β 2. Combination of the models is applied for modeling of the Internet traffic.
Physics Letters A, 2001
A question of the time the system spends in the specified state, when the final state of the syst... more A question of the time the system spends in the specified state, when the final state of the system is given, is raised. The model of weak measurements is used to obtain the expression for the time. The conditions for determination of such a time are obtained.
Physical Review E, 2005
To be published in Phys. Rev. E (2005). We present a simple point process model of 1/f β noise, c... more To be published in Phys. Rev. E (2005). We present a simple point process model of 1/f β noise, covering different values of the exponent β. The signal of the model consists of pulses or events. The interpulse, interevent, interarrival, recurrence or waiting times of the signal are described by the general Langevin equation with the multiplicative noise and stochastically diffuse in some interval resulting in the power-law distribution. Our model is free from the requirement of a wide distribution of relaxation times and from the power-law forms of the pulses. It contains only one relaxation rate and yields 1/f β spectra in a wide range of frequency. We obtain explicit expressions for the power spectra and present numerical illustrations of the model. Further we analyze the relation of the point process model of 1/f noise with the Bernamont-Surdin-McWhorter model, representing the signals as a sum of the uncorrelated components. We show that the point process model is complementary to the model based on the sum of signals with a wide-range distribution of the relaxation times. In contrast to the Gaussian distribution of the signal intensity of the sum of the uncorrelated components, the point process exhibits asymptotically a power-law distribution of the signal intensity. The developed multiplicative point process model of 1/f β noise may be used for modeling and analysis of stochastic processes in different systems with the power-law distribution of the intensity of pulsing signals.
Physical Review E, 2004
Starting from the simple point process model of 1/f noise we derive a stochastic nonlinear differ... more Starting from the simple point process model of 1/f noise we derive a stochastic nonlinear differential equation for the signal exhibiting 1/f noise in any desirably wide range of frequency. A stochastic differential equation (the general Langevin equation with a multiplicative noise) that gives 1/f noise is derived for the first time. The solution of the equation exhibits the power-law distribution. The process with 1/f noise is demonstrated by the numerical solution of the derived equation with the appropriate restriction of the diffusion of the signal in some finite interval.
Physical Review E, 2011
Probability distributions which emerge from the formalism of nonextensive statistical mechanics h... more Probability distributions which emerge from the formalism of nonextensive statistical mechanics have been applied to a variety of problems. In this paper we unite modeling of such distributions with the model of widespread 1/f noise. We propose a class of nonlinear stochastic differential equations giving both the q-exponential or q-Gaussian distributions of signal intensity, revealing long-range correlations and 1/f β behavior of the power spectral density. The superstatistical framework to get 1/f β noise with q-exponential and q-Gaussian distributions of the signal intensity in is proposed, as well.
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Papers by Bronius Kaulakys