Spectrum and Statistical Properties of Chaotic Dynamics

Quantum chaos and statistical properties of energy levels for atom in parallel electric and magnetic fields

Modern Physics Letters B ◽

10.1142/s0217984915502486 ◽

2015 ◽

Vol 29 (35n36) ◽

pp. 1550248

Author(s):

Hai-Feng Yang ◽

Yong-Gang Tan ◽

Zhong-Li Liu ◽

Hong-Zhi Fu

Keyword(s):

Magnetic Fields ◽

Quantum Chaos ◽

Chaotic Dynamics ◽

Nearest Neighbor ◽

Energy Levels ◽

Statistical Properties ◽

The Core ◽

Ideal System ◽

Electric And Magnetic Fields ◽

Diagonalization Method

In this paper, the statistical properties of energy levels are studied numerically for atom in parallel electric and magnetic fields, which is an ideal system to examine the contributions of external fields and ionic core to quantum chaos. The Stark maps of diamagnetic spectra and nearest neighbor spacing (NNS) distributions are obtained by diagonalization method incorporating core effect. We identify obvious level anti-crossing and large value of [Formula: see text] for barium, indicating that core effect has predominant contribution to chaotic dynamics in barium. To study the core effect in detail, we sweep the quantum defect artificially and find that larger core effect will undoubtedly induce stronger chaotic dynamics.

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BIFURCATION ANALYSIS OF A CIRCUIT-RELATED GENERALIZATION OF THE SHIPMAP

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127406016185 ◽

2006 ◽

Vol 16 (08) ◽

pp. 2435-2452 ◽

Cited By ~ 1

Author(s):

FEDERICO BIZZARRI ◽

MARCO STORACE ◽

LAURA GARDINI

Keyword(s):

Dynamical System ◽

Bifurcation Analysis ◽

Chaotic Dynamics ◽

Global Bifurcation ◽

Statistical Properties ◽

Point Of View ◽

Global Bifurcations ◽

Circuit Implementation ◽

Piecewise Affine ◽

Discrete Time Dynamical System

In this paper a bifurcation analysis of a piecewise-affine discrete-time dynamical system is carried out. Such a system derives from a well-known map which has good features from its circuit implementation point of view and good statistical properties in the generation of pseudo-random sequences. The considered map is a generalization of it and the bifurcation parameters take into account some common circuit implementation nonidealities or mismatches. It will be shown that several different dynamic situations may arise, which will be completely characterized as a function of three parameters. In particular, it will be shown that chaotic intervals may coexist, may be cyclical, and may undergo several global bifurcations. All the global bifurcation curves and surfaces will be obtained either analytically or numerically by studying the critical points of the map (i.e. extremum points and discontinuity points) and their iterates. In view of a robust design of the map, this bifurcation analysis should come before a statistical analysis, to find a set of parameters ensuring both robust chaotic dynamics and robust statistical properties.

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