Different Facets of Chaos in Quantum Mechanics

Nowadays there is no universally accepted definition of quantum chaos. In this paper we review and critically discuss different approaches to the subject, such as Quantum Chaology and the Random Matrix Theory. Then we analyze the problem of dynamical chaos and the time scales associated with chaos suppression in quantum mechanics. Summary: 1. Introduction 2. Quantum Chaology and Spectral Statistics 3. From Poisson to GOE Transition: Comparison with Experimental Data 3.1 Atomic Nuclei 3.2 The Hydrogen Atom in the Strong Magnetic Field 4. Quantum Chaos and Field Theory 5. Alternative Approaches to Quantum Chaos 6. Dynamical Quantum Chaos and Time Scales 6.1 Mean-Field Approximation and Dynamical Chaos 7. ConclusionsComment: RevTex, 25 pages, 7 postscript figures, to be published in Int. J. Mod. Phys.

Some open questions in "wave chaos"

The subject area referred to as "wave chaos", "quantum chaos" or "quantum chaology" has been investigated mostly by the theoretical physics community in the last 30 years. The questions it raises have more recently also attracted the attention of mathematicians and mathematical physicists, due to connections with number theory, graph theory, Riemannian, hyperbolic or complex geometry, classical dynamical systems, probability etc. After giving a rough account on "what is quantum chaos?", I intend to list some pending questions, some of them having been raised a long time ago, some others more recent

Chaos and Chaotic Phase Mixing in Galaxy Evolution and Charged Particle Beams

This paper discusses three new issues that necessarily arise in realistic attempts to apply nonlinear dynamics to galaxy evolution, namely: (i) the meaning of chaos in many-body systems, (ii) the time-dependence of the bulk potential, which can trigger intervals of {\em transient chaos}, and (iii) the self-consistent nature of any bulk chaos, which is generated by the bodies themselves, rather than imposed externally. Simulations and theory both suggest strongly that the physical processes associated with galactic evolution should also act in nonneutral plasmas and charged particle beams. This in turn suggests the possibility of testing this physics in real laboratory experiments, an undertaking currently underway.Comment: 16 pages, including 3 figures: an invited talk at the Athens Workshop on Galaxies and Chaos, Theory and Observation

Chaos and Order in Nature/Creation: A Reading of Genesis l-2:4a in Dialogue with Science and Philosophy

With inspiration from post-modern scientific theories (complexity theory, chaos theory, relativity theory, uncertainty theory, no-singularity/boundary theory), and from philosophical understandings of nature (ecstatic naturalism and Taoism), the author offers an innovative reading of the Genesis creation stories, focusing on the concepts of order and chaos. While criticizing the dichotomous dualism that underpins the human ordering system, she connects these rich meanings and wisdom signified by nature with theological discourse through a discussion of the infinity of God, the abjection of origin, the autonomy of creatures, and nature's complex and fluid manifestations.ye

Chaos Theology: A New Creation Theology and Its Applications

The problems inherent in creatio ex nihilo have led the author to the development of a new creation theology: chaos theology. Its main points are creation from an unexplained initial chaos, a remaining chaos element that is the source of physical and moral evil, and continuing creation toward fulfilment on the Last Day. Chaos theology can be reconciled with the scientific account of cosmic and biological evolution. Combining chaos theology with the physical theory of chaos helps in the understanding of God\'s action in the world. Jesus Christ is shown to be the cosmic Christ, who reconciles the entire cosmos, not only humanity. The problem of evil is readily solved in chaos theology as the effect of the remaining chaos element. From chaos theology and scientific insight in cancer, a theology of illness can be derived

Riemann zeta function and quantum chaos

A brief review of recent developments in the theory of the Riemann zeta function inspired by ideas and methods of quantum chaos is given.Comment: Lecture given at International Conference on Quantum Mechanics and Chaos, Osaka, September 200

Random Matrices and Chaos in Nuclear Spectra

We speak of chaos in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the existence of chaos be reconciled with the known dynamical features of spherical nuclei? Such nuclei are described by the shell model (a mean-field theory) plus a residual interaction. We approach the question by using a statistical approach (the two-body random ensemble): The matrix elements of the residual interaction are taken to be random variables. We show that chaos is a generic feature of the ensemble and display some of its properties, emphasizing those which differ from standard random-matrix theory. In particular, we display the existence of correlations among spectra carrying different quantum numbers. These are subject to experimental verification.Comment: 17 pages, 20 figures, colloquium article, submitted to Reviews of Modern Physic

Nonlinear and Complex Dynamics in Economics

This paper is an up-to-date survey of the state-of-the-art in dynamical systems theory relevant to high levels of dynamical complexity, characterizing chaos and near chaos, as commonly found in the physical sciences. The paper also surveys applications in economics and �finance. This survey does not include bifurcation analyses at lower levels of dynamical complexity, such as Hopf and transcritical bifurcations, which arise closer to the stable region of the parameter space. We discuss the geometric approach (based on the theory of differential/difference equations) to dynamical systems and make the basic notions of complexity, chaos, and other related concepts precise, having in mind their (actual or potential) applications to economically motivated questions. We also introduce specifi�c applications in microeconomics, macroeconomics, and �finance, and discuss the policy relevancy of chaos