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Topic: Quantum chaos

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	Quantum Chaos
		The quantum analogue of the humble pendulum is the laser; the flying cannonballs of the atomic world consist of beams of protons or electrons, and the rotating wheel is the spinning electron (the basis of magnetic tapes).
		Quantum chaos is concerned with establishing the relation between boxes P and Q. The spectrum of a chaotic quantum system was first suggested by Eugene P.
		The quantum barriers are formed by the outer layers of the sandwich, which gives the electrons a couple of straight edges to bounce back and forth between, The other edges of the table are created by the restraining effect of the magnetic field, which curves the electron motion in a complicated way.
	www.secamlocal.ex.ac.uk /people/staff/mrwatkin/zeta/quantumchaos.html (7124 words)

	Quantum Chaos
		The quantum analogue of the humble pendulum is the laser; the flying cannonballs of the atomic world consist of beams of protons or electrons, and the rotating wheel is the spinning electron (the basis of magnetic tapes).
		Quantum chaos is concerned with establishing the relation between boxes P and Q. The spectrum of a chaotic quantum system was first suggested by Eugene P.
		The quantum barriers are formed by the outer layers of the sandwich, which gives the electrons a couple of straight edges to bounce back and forth between, The other edges of the table are created by the restraining effect of the magnetic field, which curves the electron motion in a complicated way.
	secamlocal.ex.ac.uk /~mwatkins/zeta/quantumchaos.html (7124 words)

	First ever demonstration of quantum chaos during atom ionisation
		In quantum chaos research physicists are looking for similarities, in the quantum world, to the deterministic chaos of the everyday world.
		In this way, scientists at the Max Planck Institute of Quantum Optics have been investigating chaos in quantum mechanical systems that would be deterministically chaotic according to the rules of macroscopic physics.
		The chaos in the movement is demonstrated through the fact that the electron beam fluctuates in a particular way which matches the energy of the light particles.
	www.physorg.com /news7878.html (1047 words)

	Book Review of Quantum Chaos and Quantum Dots
		Quantum Chaos and Quantum Dots, written by Katsuhiro Nakamura of Osaka City University and his collaborator Takahisa Harayama, is an interesting review of some quantum-transport and related problems in solid-state systems.
		The text should prove useful to two categories of physicists: those in solid-state physics looking for an entrée to issues in quantum chaos, and those in quantum chaos interested in learning about this specific application.
		Semiconductor quantum dots are stateof- the-art structures fabricated at semiconductor heterojunctions, and consist of a mesoscopic scattering region connected to external reservoirs.
	www.aip.org /tip/breview/br22.html (594 words)

	Chaos Theory: A Brief Introduction
		The name "chaos theory" comes from the fact that the systems that the theory describes are apparently disordered, but chaos theory is really about finding the underlying order in apparently random data.
		The bifurcation diagram of the population equation is fractal.
		Chaos theory has changed the direction of science: in the eyes of the general public, physics is no longer simply the study of subatomic particles in a billion-dollar particle accelerator, but the study of chaotic systems and how they work.
	www.imho.com /grae/chaos/chaos.html (2838 words)

	Prigogine Center--Research: Quantum Chaos in Wave Guides (Site not responding. Last check: )
		As part of their on-going research into quantum chaos, Prof.
		Linda Reichl and Kyungsun Na have recently shown that in the quantum model, the conductance of the wave guide displays different features depending on whether or not the underlying classical system is integrable or non-integrable.
		The diagram at left, for example, is a numerical prediction of the probability amplitude of an electron in a "rippled chanel." The unevenness of the wave function is typical in the case where the classical Poincaré surface-of-section is chaotic.
	order.ph.utexas.edu /research/quantumchaoswaveguide.html (199 words)

	Atom Optics Group - Quantum Chaos
		The field of "quantum chaos'' was born in 1917 when Albert Einstein tried to unravel which mechanical systems can be subjected to the Bohr-Sommerfeld-Epstein quantization rules.
		One example of such features is dynamical localization, a quantum suppression of classical diffusion, which was discovered by Fishman et al in numerical studies of the periodically kicked quantum rotor.
		This is the quantum suppression of chaotic diffusion.
	www.physics.uq.edu.au /people/upcroft/source/QuantumChaos.htm (715 words)

	Physics Today January 2001
		Quantum chaos is the study of the quantum dynamics of systems that are classically chaotic.
		European institutions have discovered that quantum chaologists are fine mathematicians as well as numerical analysts, almost of necessity, and are remarkably broad in the range of applicability of their expertise.
		The maturity of the study of quantum chaos was recognized by the Nobel Foundation as recently as June 2000, when one of its Nobel Symposia was devoted to the subject.
	www.physicstoday.org /pt/vol-54/iss-1/p49b.html (745 words)

	Quantum chaos - Wikipedia, the free encyclopedia
		Quantum chaos is an interdisciplinary branch of physics, arising from so-called semi-classical models.
		The foundations of modern quantum mechanics were laid in that period, essentially leaving aside the issue of the quantum-classical correspondence in systems whose classical limit exhibits chaos.
		Its emergence in the second half of the twentieth century was aided to a large extent by renewed interest in classical nonlinear dynamics (chaos theory), and by quantum experiments bordering on the macroscopic size regime where laws of classical mechanics are expected to emerge.
	en.wikipedia.org /wiki/Quantum_chaos (635 words)

	Brain, Chaos, Quantum Mechanics
		The occurrence of chaos in neurosystem dynamics suggests that the brain may also utilize the fractal aspect of chaos as an intrinsic aspect of its processing, in combination with the natural scale transformations from organism to cell to molecule.
		Both these authors adhere to the Everett many-worlds interpretation of quantum mechanics in which the collapse of the wave function never occurs, and all histories having a non-zero probability under the quantum prediction are presumed to co-exist as parallel aspects of a cosmic wave function.
		Such time-reversal is used in the transactional interpretation of quantum mechanics (Cramer 1986) fig 14(c), a mutual encounter between emitter and absorber is modelled by the release of crossed-phase advanced and retarded waves, each having zero-energy, the offer wave of the emitter and the confirmation wave of the absorber.
	uncletaz.com /library/scimath/brainchaos.html (14348 words)

	Quantum Mechanics & Chaos Theory: Anarchist Meditations on N. Herbert's Quantum Reality: Beyond the New Physics
		Quantum Mechanics (QM), considered as the source of such a paradigm, at first seems to lack any social ramifications or parallels, almost as if its very weirdness deprives it of all connnections with "everyday" life or social reality.
		Chaos Theory, like any good theory, can be applied to anything, from physics to literary criticism -- just as it can absorb energy from any kind of source, from the heretical spiritual teachings of sufis, Ismailis, Ranters, shamans or sorcerers -- to QM itself.
		Chaos theory seems to predict that Quantum Theory will flourish as long as it remains "incomplete," not tied down on any Classical (or even non-Boolean) procrustrean beds-metalogical, metalinguistic, essentially unstructured -- "free," like reality itself -- which is a state not of Anarchism but of anarchy, even to the very roots of being.
	www.hermetic.com /bey/quantum.html (2819 words)

	Quantum Chaos in Helium
		Now, an investigation into the transition from quantum dynamics to chaos in the spectrum of helium has shed a little bit of light on one of physics’s flest boxes—quantum chaos.
		Furthermore, the quantum states of the helium atom, the prototypical three-body charged-particle system, occur in seemingly regular progressions, labeled by sets of quantum numbers.
		Thus, understanding chaos, both in the realm of the familiar classical mechanics and in the realm of quantum mechanics, is key to understanding the dynamics of our world.
	www-als.lbl.gov /als/science/sci_archive/47Qchaos.html (969 words)

	Theoretical Reseach - UMD Chaos Group
		Recently it has been shown that chaos in the Lagrangian dynamics of the underlying flow is the key consideration for answering the question posed by the kinematic dynamo problem.
		The study of how quantum systems, whose classical counterparts are chaotic, behave in the semiclassical limit has been called quantum chaos.
		Among recent results in quantum chaos is a prediction relating the chaos in the classical problem to the statistics of energy-level spacings in the semiclassical quantum regime.
	www-chaos.umd.edu /research.html (1830 words)

	The Quantum Chaos Group
		The Quantum Chaos Group in the Department of Physics at The University of Auckland, comprises eight members led by Professor Rainer Leonhardt, who collectively examine the difference in behaviour between quantum mechanical systems and the corresponding classical systems.
		Quantum chaos is the study of how quantum systems can mimic classical chaotic dynamics.
		However, chaos does exist in the everyday (classical) world and since classical mechanics is just a limiting case of quantum mechanics, this chaotic behaviour should be inherent in quantum mechanics also.
	www.phy.auckland.ac.nz /atomtrapping (172 words)

	Fractal Neurodyamics and Quantum Chaos/1
		The stochastic nature of the theory makes it possible in effect for each quantum to both be conscious of the universe through the extended wave function and to exercise free-will in its demise in wave packet reduction, while conforming to the principles of quantum mechanics.
		While some aspects of mind, such as visual processing, have structural stability in their representation of most objects, optical illusions and a variety of mental phenomena from hallucinations to the bizarre subjective realities of dreaming sleep demonstrate that the mind is capable of unstable self-generative behavior.
		Chaos in this state enables the system to explore its phase space, falling into an existing attractor in the case of a recognised odour, but bifurcating to form a new attractor in the case of a newly learned stimulus.
	www.dhushara.com /book/paps/consc/brcons1.htm (8684 words)

	Science News Magazine Editor's Picks - Cavities of chaos
		Several research groups are studying microwaves in thin, metallic boxes and electrons in tiny structures called quantum dots to verify theoretical results and to explore the possibility of unveiling new physics not yet evident to the theorists.
		To explore the manifestations of chaos in quantum mechanics, Srinivas Sridhar, Arshad Kudrolli, and their coworkers at Northeastern University in Boston observe the behavior of microwaves in closed, shallow copper containers, or cavities.
		In the quantum world, these normal modes are known as eigenfunctions, and Sridhar has developed a way to map the eigenfunctions of microwaves bouncing around inside cavities of different shapes.
	www.sciencenews.org /sn_edpik/ps_1.htm (1292 words)

	Quantum Chaos
		Quantum mechanics, as it has been practiced for about 90 years, belongs in the third compartment, caned Q. After the pioneering work of Planck, Einstein and Niels Bohr.
		This behaviour of quantum systems is often attreibuted to a special property of the quantlani equations: their linearity.
		Berry's preferred explanation for the difference between what happens in classical and qtiaiitum systenis as they edge towards chaos is that quantum uncertainty iniposes a fundamental limit on the sharpness of the dynamics.
	www.dhushara.com /book/quantcos/qchao/quantc.htm (7426 words)

	CHAOS - CLASSICAL AND QUANTUM: unstable postscript version
		We first recapitulate basic notions of quantum mechanics and define the main quantum objects of interest, the quantum propagator and the Green's function.
		This is what could have been done with the old quantum mechanics if physicists of 1910's were as familiar with chaos as you by now are.
		A brief review of the quantum theory of elastic scattering of a point particle from a repulsive potential, and its connection to the Gutzwiller theory for bound systems.
	chaosbook.org /postscript.shtml (1356 words)

	Quantum Chaos (Site not responding. Last check: )
		As the magnetic field is tilted away from the applied electric field, the classical dynamics become increasingly chaotic.
		Even quite far from bifurcations,in the experiment the contribution from the s' PO is in general not isolated from 2t-0 since they have similar actions) 2) most data corresponds to the mixed phase-space regime where there are cascades of bifurcations, with important contributions from 'ghost' POs and non-generic types of bifurcation.
		We found that a theory based on a novel type of complex (ie with imaginary time and coordinates), non-periodic 'Saddle Orbit' provides an analytical formula which acurately predicts the phase and amplitude of observed oscillations in the tunnelling current: it does not break down at PO bifurcations/ ghosts and is nearly always isolated.
	www.tampa.phys.ucl.ac.uk /tania/CHAOS/RTD.html (282 words)

	Quantum Chaos - Cambridge University Press (Site not responding. Last check: )
		Quantum Chaos provides a comprehensive overview of our understanding of chaotic behaviour in a wide variety of quantum and semiclassical systems, and describes both experimental and theoretical investigations.
		Thereafter, in an authoritative collection of papers, prominent scientists put forward their particular interpretations of quantum chaos, with reference to a broad range of interesting physical systems.
		Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Kuchiev and O. Sushkov; 18.
	www.cambridge.org /catalogue/catalogue.asp?isbn=052143291X (668 words)

	Quantum Chaos
		At the end of the 19th century the American astronomer William Hill demonstrated that the irregularity is the reswt entirelly of the gravitational pull of the sun.
		This behaviour of quantum systems is often attreibuted to a special property of the quantlani equations: their linearity.
		Berry's preferred explanation for the difference between what happens in classical and qtiaiitum systenis as they edge towards chaos is that quantum uncertainty iniposes a fundamental limit on the sharpness of the dynamics.
	dhushara.tripod.com /book/quantcos/qchao/quantc.htm (7387 words)

	Quantum Chaos Tutorial
		Since all tiny particles must follow the rules of quantum mechanics, and since all matter is thought to be composed of tiny particles, the rules of classical mechanics that are followed by large objects must somehow arise from the rules of quantum mechanics.
		Another approach to the problem of quantum chaos is to formulate a probabilistic description of classical mechanics and attempt to find a definition of chaos that works in this new context.
		A third approach to the problem of quantum chaos is to ignore the question of defining chaos in quantum mechanics and instead concentrate on identifying features of a quantum system that correspond to chaos in a classical system.
	fsweb.berry.edu /academic/mans/ttimberlake/qchaos/qchaos.html (874 words)

	ScienceDaily: Quantum Computer Articles
		Quantum entanglement is a quantum mechanical phenomenon in which the quantum states of two or more objects have to be described with reference to each other, even though the individual objects may be...
		A quantum dot is a semiconductor nanostructure that confines the motion of conduction band electrons, valence band holes, or excitons (bound pairs of conduction band electrons and valence band holes)...
		Quantum mechanics is a fundamental branch of theoretical physics that replaces Newtonian mechanics and classical electromagnetism at the atomic and subatomic levels.
	www.sciencedaily.com /articles/computers_math/quantum_computers (508 words)

	Chaos theory - Wikipedia, the free encyclopedia
		The first discoverer of chaos can plausibly be argued to be Jacques Hadamard, who in 1898 published an influential study of the chaotic motion of a free particle gliding frictionlessly on a surface of constant negative curvature.
		Chaos theory progressed more rapidly after mid-century, when it first became evident for some scientists that linear theory, the prevailing system theory at that time, simply could not explain the observed behavior of certain experiments like that of the logistic map.
		The term chaos as used in mathematics was coined by the applied mathematician James A. Yorke.
	en.wikipedia.org /wiki/Chaos_theory (2171 words)

	Abarim Publications: Quantum Mechanics, Chaos Theory and the Reliability of the Bible
		Quantum Mechanics and Chaos Theory shed new and surprising light on major Biblical events, such as the creation, the crucifixion and resurrection of Jesus Christ, the nature of God, man and the universe.
		The emergence of Jesus Christ and the church of Jesus Christ on the terrestrial surface was preceded and is explained by highly similar events in the material universe.
		Quantum Mechanics studies the peculiar world of the "ones"; those things in nature that can not be divided.
	www.abarim-publications.com (412 words)

	Quantum Chaos
		Quantum Chaos, which is a relatively new research field, deals with how classical chaos systems behave in quantum mechanics.
		The symposium focused mainly on experiments and theory and on the interplay between them, emphasizing the interdisciplinary nature of the subject and discussing the impact of quantum chaos on such fields as atomic, nuclear and solid state physics.
		The physical principles behind quantum chaos have much in common with acoustics, microwaves and optics, as several lectures pointed out.
	www.nobelprize.org /nobelfoundation/symposia/physics/ns116/about.html (201 words)

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