1,118 research outputs found
Layered Chaos in Mean-field and Quantum Many-body Dynamics
We investigate the dimension of the phase space attractor of a quantum
chaotic many-body ratchet in the mean-field limit. Specifically, we explore a
driven Bose-Einstein condensate in three distinct dynamical regimes - Rabi
oscillations, chaos, and self-trapping regime, and for each of them we
calculate the correlation dimension. For the ground state of the ratchet formed
by a system of field-free non-interacting particles, we find four distinct
pockets of chaotic dynamics throughout these regimes. We show that a
measurement of a local density in each of the dynamical regimes, has an
attractor characterized with a higher fractal dimension, ,
, and , as compared to the global measure
of current, , , and .
We find that the many-body case converges to mean-field limit with strong
sub-unity power laws in particle number , namely with
, and
for each of the dynamical regimes mentioned above.
The deviation between local and global measurement of the attractor's dimension
corresponds to an increase towards high condensate depletion which remains
constant for long time scales in both Rabi and chaotic regimes. The depletion
is found to scale polynomially with particle number as with
and for the two regimes.
Thus, we find a strong deviation from the mean-field results, especially in the
chaotic regime of the quantum ratchet. The ratchet also reveals quantum
revivals in the Rabi and self-trapped regimes but not in the chaotic regime.
Based on the obtained results we outline pathways for the identification and
characterization of the emergent phenomena in driven many-body systems
Power-Law Sensitivity to Initial Conditions within a Logistic-like Family of Maps: Fractality and Nonextensivity
Power-law sensitivity to initial conditions, characterizing the behaviour of
dynamical systems at their critical points (where the standard Liapunov
exponent vanishes), is studied in connection with the family of nonlinear 1D
logistic-like maps The main ingredient of our approach is the generalized deviation
law \lim_{\Delta x(0) -> 0} \Delta x(t) / \Delta x(0)} = [1+(1-q)\lambda_q
t]^{1/(1-q)} (equal to for q=1, and proportional, for large
t, to for is the entropic index appearing in
the recently introduced nonextensive generalized statistics). The relation
between the parameter q and the fractal dimension d_f of the onset-to-chaos
attractor is revealed: q appears to monotonically decrease from 1
(Boltzmann-Gibbs, extensive, limit) to -infinity when d_f varies from 1
(nonfractal, ergodic-like, limit) to zero.Comment: LaTeX, 6 pages , 5 figure
Chaotic Time Series Analysis in Economics: Balance and Perspectives
To show that a mathematical model exhibits chaotic behaviour does not prove that chaos is also present in the corresponding data. To convincingly show that a system behaves chaotically, chaos has to be identified directly from the data. From an empirical point of view, it is difficult to distinguish between fluctuations provoked by random shocks and endogenous fluctuations determined by the nonlinear nature of the relation between economic aggregates. For this purpose, chaos tests test are developed to investigate the basic features of chaotic phenomena: nonlinearity, fractal attractor, and sensitivity to initial conditions. The aim of the paper is not to review the large body of work concerning nonlinear time series analysis in economics, about which much has been written, but rather to focus on the new techniques developed to detect chaotic behaviours in the data. More specifically, our attention will be devoted to reviewing the results reached by the application of these techniques to economic and financial time series and to understand why chaos theory, after a period of growing interest, appears now not to be such an interesting and promising research area.Economic dynamics, nonlinearity, tests for chaos, chaos
Real-time support for high performance aircraft operation
The feasibility of real-time processing schemes using artificial neural networks (ANNs) is investigated. A rationale for digital neural nets is presented and a general processor architecture for control applications is illustrated. Research results on ANN structures for real-time applications are given. Research results on ANN algorithms for real-time control are also shown
Dissipative Chaos in Semiconductor Superlattices
We consider the motion of ballistic electrons in a miniband of a
semiconductor superlattice (SSL) under the influence of an external,
time-periodic electric field. We use the semi-classical balance-equation
approach which incorporates elastic and inelastic scattering (as dissipation)
and the self-consistent field generated by the electron motion. The coupling of
electrons in the miniband to the self-consistent field produces a cooperative
nonlinear oscillatory mode which, when interacting with the oscillatory
external field and the intrinsic Bloch-type oscillatory mode, can lead to
complicated dynamics, including dissipative chaos. For a range of values of the
dissipation parameters we determine the regions in the amplitude-frequency
plane of the external field in which chaos can occur. Our results suggest that
for terahertz external fields of the amplitudes achieved by present-day free
electron lasers, chaos may be observable in SSLs. We clarify the nature of this
novel nonlinear dynamics in the superlattice-external field system by exploring
analogies to the Dicke model of an ensemble of two-level atoms coupled with a
resonant cavity field and to Josephson junctions.Comment: 33 pages, 8 figure
Chaos Attractors as an Alignment Mechanism between Projects and Organizational Strategy
AbstractChaos attractors have been studied in detail in the biological and environmental sciences and used to explain phenomena such as the Butterfly effect. Limited research has been done to identify and understand the use of chaos attractors in projects to help with alignment of project activities towards the project objective throughout the entire project duration. This paper will explore the literature on the use of chaos attractors as alignment mechanism between projects and organizational strategy. A conceptual model and propositions are proposed that could form the basis for further research
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