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1
Content available remote

Turbulence in the One-Dimensional Complex Ginzburg-Landau Equation

100%
Zubrzycki A.
Acta Physica Polonica A
|
1995
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vol. 87
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issue 6
925-932
EN
The transition to phase and amplitude turbulent states in the one-dimen­sional complex Ginzburg-Landau equation is investigated by a numerical simulation. In order to describe existing attractors quantitatively, the largest Lyapunov exponent is estimated. The largest Lyapunov exponent is positive but small for the phase turbulence and it is much larger for the amplitude turbulence. Moreover, it seems independent on the system size.
2
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Peano Dynamics as a Model for Turbulence and Strange Nonchaotic Behaviour

100%
El Naschie M.
Acta Physica Polonica A
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1991
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vol. 80
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issue 1
3-13
EN
The note outlines a scenario for a two-dimensional dynamic system to possess strange nonchaotic behaviour in the presence of two frequency quasi periodic forcing. Implications for turbulence are also discussed.
3
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Spatio-Temporal Dynamics of Chain of Coupled Impact Pendulums

100%
Stępień R., Kosiński R. A.
Acta Physica Polonica A
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1997
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vol. 91
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issue 6
1053-1059
EN
A chain of N, one-dimensional, impact pendulums is investigated using numerical solutions of equations of motion. Ranges of periodic, mixed and chaotic motion are found using spatio-temporal diagrams. A correlation function and power spectrum density functions are calculated for these digitized diagrams. Influence of the coupling strength k and the number of pendulums N on the dynamics of the system is discussed.
4
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Application of Time-Delay Reconstruction Method for Examination of Spatial Inhomogeneity of Dynamical Systems

100%
Zubrzycki A., Sukiennicki A.
Acta Physica Polonica A
|
1997
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vol. 91
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issue 6
1043-1052
EN
Three spatially extended one-dimensional dynamical systems are examined by numerical simulations and the time-delay technique is applied to find their dynamics at different positions in space. On the basis of this technique the correlation dimension is calculated from time series obtained at different positions. It is found that the value of the correlation dimension may vary from one position to another, reflecting the spatial inhomogeneity of the system.
5
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Quantum Implications of Ray Splitting

100%
Blümel R.
Acta Physica Polonica A
|
1998
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vol. 93
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issue 1
7-10
EN
Ray splitting is a universal phenomenon that occurs in all wave systems with sharp interfaces. Quantum implications of ray splitting are: (i) the importance of non-Newtonian orbits for the density of states in the semiclassical limit, (ii) ray-splitting corrections to the average density of states and (iii) the need to include non-Newtonian orbits in trace formulas for the oscillating part of the density of states. The signatures of non-Newtonian orbits in the density of states have recently been identified experimentally.
6
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Spatial Inhomogeneity of Periodic and Chaotic Attractors of a Driven Damped Nonlinear Schrödinger Equation

100%
Zubrzycki A.
Acta Physica Polonica A
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1995
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vol. 88
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issue 6
1067-1072
EN
The driven damped nonlinear Schrödinger equation is solved numeri­cally and different attractors - periodic and chaotic ones - are obtained for different ranges of the forcing field amplitude. It is shown that these attrac­tors are in both cases spatially nonuniform in time. Spatial inhomogeneity of the chaotic attractor is investigated by the estimation of the correlation dimension at different space points.
7
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Homoclinic Chaos in Generalized Henon-Heiles System

100%
Kasperczuk S.
Acta Physica Polonica A
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1995
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vol. 88
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issue 6
1073-1080
EN
This paper considers the generalized Henon-Heiles system, defined by the Hamiltonian Η = (p^{2}_{1} + p^{2}_{2} + Αq^{2}_{1} + Bq^{2}_{2})/2 + Cq^{2}_{1}q_{2} + Dq^{3}_{2}. Melnikov's method is used to prove the existence of nondegenerate homoclinic orbits near two integrable cases: (o) C = 0; A, B, D arbitrary; (i) A = B; C = 3D. The existence of such orbits precludes the existence of analytic second integrals.
8
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Autocorrelation Function and Mutual Information from Short Experimental Time Series

100%
Zduniak A., Łusakowski J.
Acta Physica Polonica A
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1995
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vol. 87
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issue 1
257-260
EN
A nonlinear dynamics of self-generated current oscillations in semi-insu­lating GaAs was studied by the reconstruction of an attractor from a short (14500 points) time series. Two methods of choosing of a time constant (τ) for this reconstruction are compared. One of them assumes τ to be an argu­ment of the first zero of the autocorrelation function and the other takes τ as an argument of the first minimum of the mutual information. It is shown that for periodic oscillations both methods are equivalent, but for chaotic ones only the mutual information gives a time constant which does not depend on a time series used for calculations.
9
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On Electrons in Quantum Chaos State in Doped Fullerene Crystal

63%
Koper A., Mucha M.
Acta Physica Polonica A
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2000
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vol. 97
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issue 1
229-232
EN
We show that band electrons in A_{n}C_{60} crystal (C_{60} fullerene doped with alkali ions A) are in highly chaotic quantum state. We describe intensity of the chaos by means of the Shannon information entropy, which we calculate using single particle Bloch functions. The entropy provides a quantitative measure of scars as well as degree of electrons delocalization in gaps between C_{60} molecules. Implications of our results for conductivity in A_{3}C_{60} are discussed.
10
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Classical Paths and Semiclassical Ghosts

63%
Haake F.
Acta Physica Polonica A
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1994
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vol. 85
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issue 4
693-698
EN
The semiclassical approximation for the quantum propagator of the kicked top is shown to involve not only classical periodic orbits but also complex generalizations thereof. Such ghost trajectories have complex actions S and thus contribute exponentially small terms as ħ → O. However, close to bifurcations ImS can be very small whereupon ghosts become quite visible.
11
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Regular and Chaotic Behaviour of a Kicked Damped Spin

63%
Hołyst J., Sukiennicki A.
Acta Physica Polonica A
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1992
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vol. 81
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issue 3
353-360
EN
The dynamics of a kicked, anisotropic, damped spin is reduced to a two-dimensional map. This map exhibits such features as bifurcation diagrams, regular or chaotic attractors/repellors and intermittent-like transitions between two strange attractors. With increase of damping a transition from chaos to the fixed point attractor occurs. On the contrary to the Hamiltonian case the type of magnetic anisotropy plays a crucial role for damped models.
12
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Stochastic Resonance in System with On-Off Intermittency

63%
Krawiecki A.
Acta Physica Polonica A
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1997
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vol. 92
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issue 6
1101-1108
EN
Stochastic resonance in a chaotic threshold-crossing system exhibiting on-off intermittency and attractor bubbling: the logistic map with the control parameter varying randomly or chaotically in time is studied in the case of weak additive and multiplicative periodic forcing. In both cases signal-to-noise ratio shows dependence on the forcing frequency; in the case of multiplicative forcing this dependence appears even for very small frequencies. It is shown that this is a result of a very long characteristic time scale, typical of systems with on-off intermittency.
13
Content available remote

Non Saturation of Energy in a Quantum Kicked Oscillator

63%
Daly M., Hefernan D.
Acta Physica Polonica A
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1996
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vol. 89
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issue 5-6
571-580
EN
We present a quantum mapping for the kicked harmonic oscillator which relates the probability amplitudes of the undriven oscillator's eigenfunctions over successive kicks. We show how for various kick strengths the wave functions have a linear energy increase up to the limit imposed by the finite matrix size of the evolution matrix. We use this linear energy increase to define a quantum diffusion-like coefficient. We also show how this increase in energy causes the wave functions to spread out and become diffuse with little or no discernible structure. This model may serve as a paradigm for the study of quantum chaos.
14
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Fractal Dimensions from Chaotic Oscillations in Semi-Insulating GaAs

63%
Zduniak A., Łusakowski J.
Acta Physica Polonica A
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1993
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vol. 84
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issue 3
575-578
EN
Relaxation and domain current oscillations in undoped semi-insulating GaAs were observed at room temperature for a broad range of voltage applied to a sample. The oscillations were characterized by a reconstruction of an attractor of the system. An analysis of the attractor helped to discriminate between the two likes of oscillations. A transition from one like of oscillations to the other was connected with a chaotization of the current. A chaotic state of the system was analyzed by calculations of fractal dimensions D_{q} for -0.6 < g < 40 and the f(α) function.
15
Content available remote

Chaos Assisted Tunneling and Nonspreading Wave Packets

51%
Zakrzewski J., Delande D., Buchleitner A.
Acta Physica Polonica A
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1998
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vol. 93
|
issue 1
179-186
EN
Consider an initial state lying on a primary resonance island. The state may tunnel into the chaotic sea surrounding it and further escape to infinity via chaotic diffusion. Properties of transport in such a situation are studied on an exemplary system - the hydrogen atom driven by microwaves. We show that the combination of tunneling followed by chaotic diffusion leads to peculiar large scale fluctuations of the AC Stark shift and ionization rates. An appropriate random matrix model describes accurately these statistical properties.
16
Content available remote

Polarization Dependence of Microwave "ionization" of Excited Hydrogen Atoms

51%
Koch P.
Acta Physica Polonica A
|
1998
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vol. 93
|
issue 1
105-133
EN
After a brief review of the ionization of excited hydrogen atoms by a linearly polarized field, we discuss experimental results for the polarization dependence of this process. Experiments at ω/2π = 9.904 GHz used two different ranges of principal quantum number n_{0} between 29 and 98. At low scaled frequencies, Ω ≲ 0.1, ionization data for certain narrow ranges of n_{0} exhibit striking sensitivity to fields with elliptical polarization not too far from circular polarization. Classical calculations reproduce this behavior and show it to be the result of 2ω driving terms that appear when the Hamiltonian is transformed to a frame rotating at ω. It shows how higher-dimensional dynamics can influence the ionization and be used to control it when the polarization departs from linear or circular polarization. At higher scaled frequencies, 0.6 ≲ Ω_{0} ≲ 1.4, near the onset of ionization circularly and elliptically polarized data show surprising similarities with linearly polarized data in a parameter regime where the ionization dynamics is dominated by the influence of the pendulumlike resonance zone centered at scaled frequency n_{0}^{3}ω ≡ Ω_{0} = 1. The stabilizing influence of this zone can be understood classically, but nonclassical stability associated with quantal separatrix states at its edge is a semiclassical effect.
17
Content available remote

Chaotic Dynamics of Domain Walls in Magnetic Garnet Films with In-Plane Fields

51%
Sukiennicki A., Kosiński R.
Acta Physica Polonica A
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1995
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vol. 87
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issue 6
933-938
EN
Chaotic dynamics and routes to chaos of domain walls in magnetic bub­ble garnet materials in the presence of in-plane fields were investigated nu­merically using Slonczewski's equations of motion. Connection between the structure of the wall and the character of the attractor was found. The in-plane field can play a role of the factor controlling chaos.
18
Content available remote

On-Off Intermittency in Randomly Driven Parallel Pumping

51%
Krawiecki A.
Acta Physica Polonica A
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1997
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vol. 92
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issue 2
465-468
EN
A model of parallel pumping with many interacting parametric spin-wave pairs is investigated numerically. On-off intermittency is obtained in the time series of absorption when the rf field amplitude is varied randomly in time, slowly in comparison with the rf field frequency, and when its mean value exceeds slightly the parallel pumping instability threshold. If the interactions between parametrically and thermally excited spin waves are neglected, only one parametric spin-wave pair is strongly excited and exhibits intermittent behaviour. In the opposite case a packet of parametric spin waves with frequencies close to half the pumping frequency may be excited. This modifies quantitatively, but not qualitatively the intermittency characteristics in the presence of thermal noise.
19
Content available remote

Simulations of Noise-Free Stochastic Resonance in Spin-Wave Chaos

51%
Krawiecki A., Reibold E., Benner H., Sukiennicki A.
Acta Physica Polonica A
|
2000
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vol. 97
|
issue 5
975-978
EN
Numerical simulations of noise-free stochastic resonance and aperiodic stochastic resonance in chaotic ferromagnetic resonance are presented. The model, based on three-magnon interactions between the externally excited uniform mode and pairs of spin waves, shows on-off intermittency. The rf magnetic field amplitude is slowly modulated by a small periodic or aperiodic signal, and the output signal, which reflects the occurrence of laminar phases and bursts in the time series of spin-wave amplitudes, is analyzed. On variation of the dc magnetic field the signal-to-noise ratio of the output signal and the correlation function between modulation and output signal pass a maximum, which indicates the occurrence of periodic and aperiodic stochastic resonance, respectively. The role of thermal magnon excitations in the occurrence of this maximum is clarified. The results are compared with experimental findings obtained in other types of intermittency.
20
Content available remote

Chaotic Dynamics of Periodically Driven Domain Walls in Magnetic Garnet Films

51%
Kosiński R., Sukiennicki A.
Acta Physica Polonica A
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1996
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vol. 89
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issue 4
495-501
EN
The motion of domain walls in thin garnet films was investigated numerically using Slonczewski's equations of wall motion for the case of periodic drive field. The type of the wall motion was analyzed by observation of phase trajectories and spatio-temporal diagrams. It was found that depending on the period and amplitude of the drive field the motion of the wall is periodic or chaotic, reflecting the character of the dynamical processes connected with horizontal Bloch lines in the wall.
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