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151.
B. Jourdain 《Methodology and Computing in Applied Probability》2000,2(1):69-91
In this paper, we explain how to associate a nonlinear martingale problem with some nonlinear parabolic evolution equations starting at bounded signed measures. Our approach generalizes the classical link made when the initial condition is a probability measure. It consists in giving to each sample-path a signed weight which depends on the initial position. After dealing with the classical McKean-Vlasov equation as an introductory example, we are interested in a viscous scalar conservation law. We prove uniqueness for the corresponding nonlinear martingale problem and then obtain existence thanks to a propagation of chaos result for a system of weakly interacting diffusion processes. Last, we study the behavior of the associated fluctuations and present numerical results which confirm the theoretical rate of convergence. 相似文献
152.
We investigate the quantum-classical transition of a kicked rotor (KR) under perturbation by a second one. The influence of such a chaotic KR makes decoherence of the first one, resulting in the emergence of classical diffusion from its quantum dynamics. Such quantum-classical transition persists by decreasing the effective Planck's constant h, and at the same time, decreasing the mass of the second KR and the interaction strength proportionally. In the limit of h → 0, due to vanishing small mass and interaction, the second KR has almost no effect on the classieal dynamics of the first one. We demonstrate this via two different coupling potentials. 相似文献
153.
Yu. A. Dabaghian 《Theoretical and Mathematical Physics》2008,156(1):996-1019
We discuss how to obtain exact and approximate distributions for various statistical characteristics of the spectra of quantum
graphs using previously found exact solutions of the spectral problem. We indicate the relation between the appearing spectral
decompositions and the theory of weakly dependent random variables and indicate the relation between the known limit theorems
for trigonometric sums and the universal statistical properties of the spectra of quantum chaotic systems.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 1, pp. 38–66, July, 2008. 相似文献
154.
WANG Zhi-Xiu ZHANG Xi-He SHEN Ke 《理论物理通讯》2008,50(7):215-219
The spatial structure of a Bose-Einstein condensate (BEC) loaded into an optical lattice potential is investigated and the spatially chaotic distributions of the condensates are revealed. A method of chaos control with linear feedback is presented in this paper. By using the method, we propose a scheme of controlling chaotic behavior in a BEC with atomic mirrors. The results of the computer simulation show that controlling the chaos into the stable states could be realized by adjusting the coefficient of feedback only if the maximum Lyapunov exponent of the system is negative. 相似文献
155.
A new type of crisis is shown to exist in a broad class of systems (including the Lorenz model) which leads to an anomalous band splitting or to a symmetry-breaking bifurcation of the strange attractor, depending on the actual values of the control parameters. A piecewise linear model is used to understand the mechanism of this crisis and to obtain exact results. 相似文献
156.
157.
We investigate the construction of low-dimensional spatiallylocalized models of extended systems. Specifically, theKuramoto–Sivashinsky (KS) equation on large one-dimensional domainsdisplays spatiotemporally complex dynamics that are remarkablywell-localized in both real and Fourier space, as demonstrated by a(spline) wavelet representation. We show how wavelet projectionsmay be used to construct various localized, relativelylow-dimensional models of KS spatiotemporal chaos. There ispersuasive evidence that short, periodized systems, internally forcedat their largest scales, form minimal models for chaotic dynamics inarbitrarily large domains. Such models assist in the understandingof extended systems. 相似文献
158.
The dynamical properties of Rydberg hydrogen atom near a metal surface are presented by using the methods of phase space analysis
and closed orbit theory. Transforming the coordinates of the Hamiltonian, we find that the phase space of the system is divided
into vibrational and rotational region. Both the Poincaré surface of section and the closed orbit theory verify the same conclusion
clearly. In this paper we choose the atomic principal quantum number asn=20. The dynamical character of the exited hydrogen atom depends sensitively on the atom-surface distanced. Whend is sufficiently large, the atom-surface potential can be expressed by the traditional van der Waals force and the system
is integrable. Whend becomes smaller, there exists a critical valued
c. Ford>d
c, the system is near-integrable and the motion is regular. While chaotic motion appears ford<d
c, and the system tends to be non-integrable. The trajectories become unstable and the electron might be captured onto the
metal surface. 相似文献
159.
A. Robledo 《Pramana》2005,64(6):947-956
We recall that at both the intermittency transitions and the Feigenbaum attractor, in unimodal maps of non-linearity of order
ζ > 1, the dynamics rigorously obeys the Tsallis statistics. We account for theq-indices and the generalized Lyapunov coefficients λq that characterize the universality classes of the pitchfork and tangent bifurcations. We identify the Mori singularities
in the Lyapunov spectrum at the onset of chaos with the appearance of a special value for the entropic indexq. The physical area of the Tsallis statistics is further probed by considering the dynamics near criticality and glass formation
in thermal systems. In both cases a close connection is made with states in unimodal maps with vanishing Lyapunov coefficients. 相似文献
160.
The spatial structure of a Bose-Einstein Condensate (BEC) loaded into an optical lattice potential is investigated. We suggest
a method for generating chaos in BEC by modulating periodic signals to convert the regular states into chaotic states. The
maximal Lyapunov exponent is calculated as a function of modulation intensity and modulation frequency respectively, and the
chaotic orbits associated with the positive Lyapunov exponents.
相似文献