Ebook: Chaotic Behavior in Quantum Systems: Theory and Applications

Six years ago, in June 1977, the first international conference on chaos in classical dynamical systems took place here in Como. For the first time, physicists, mathematicians, biologists, chemists, economists, and others got together to discuss the relevance of the recent progress in nonlinear classical dynamics for their own research field. Immediately after, pUblication of "Nonlinear Science Abstracts" started, which, in turn, led to the Physica D Journal and to a rapid increase of the research activity in the whole area with the creation of numerous "Nonlinear Centers" around the world. During these years great progress has been made in understanding the qualitative behavior of classical dynamical systems and now we can appreciate the beautiful complexity and variety of their motion. Meanwhile, an increasing number of scientists began to wonder whether and how such beautiful structures would persist in quantum motion. Indeed, mainly integrable systems have been previously con­ sidered by Quantum Mechanics and therefore the problem is open how to describe the qualitative behavior of systems whose classical limit is non-integrable. The present meeting was organized in view of the fact that scientists working in different fields - mathematicians, theoretical physicists, solid state physicists, nuclear physicists, chemists and others - had common problems. Moreover, we felt that it was necessary to clarify some fundamental questions concerning the logical basis for the discussion including the very definition of chaos in Quantum Mechanics.

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Content:
Front Matter....Pages i-viii
Mathematical and Physical Properties of Schrodinger Equations with Random and Almost-Periodic Potentials....Pages 1-10
Small Divisors in Quantum Mechanics....Pages 11-35
The Relation Between Quantum Mechanics And Classical Mechanics: A Survey Of Some Mathematical Aspects....Pages 37-76
Lifshitz Singularity of the Integrated Density of States and Absence of Diffusion Near the Bottom of the Spectrum for A Random Hamiltonian....Pages 77-82
Fluctuations in Nuclear Spectra....Pages 83-101
Characterization of Fluctuations of Chaotic Quantum Spectra....Pages 103-111
Spectral Fluctuations and Chaos in Quantum Systems....Pages 113-122
Aspects of Degeneracy....Pages 123-140
Periodic Orbits and a Correlation Function for the Semiclassical Density of States....Pages 141-147
Mild Chaos....Pages 149-164
Regular and Irregular Energy Spectra....Pages 165-170
Stochastic Ionization of Bound Electrons....Pages 171-186
Quantum Diffusion Limitation at Excitation of Rydberg Atom in Variable Field....Pages 187-204
Quantum Chaos and Anderson Localization....Pages 205-216
Transition of a Coherent Classical Wave to Phase Incoherence....Pages 217-225
Chaos in Dissipative Quantum Systems....Pages 227-233
Semiclassical Quantization on Fragmented Tori....Pages 235-254
Quantum Ergodicity And Intensity Fluctuations....Pages 255-292
Aspects of Intramolecular Dynamics in Chemistry....Pages 293-298
Semiclassical Analysis of Regular and Irregular Modes of Quantum Coupled Oscillators....Pages 299-308
Quantum Chaos as Basis for Statistical Mechanics....Pages 309-319
Continual Observations in Quantum Mechanics....Pages 321-344
Classical Quantization: Two Possible Approaches....Pages 345-351
Quantum Chaos and the Theory of Measurement....Pages 353-361
Bohr’s “Phenomenon” and “Law Without Law”....Pages 363-378
Back Matter....Pages 379-380

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Content:
Front Matter....Pages i-viii
Mathematical and Physical Properties of Schrodinger Equations with Random and Almost-Periodic Potentials....Pages 1-10
Small Divisors in Quantum Mechanics....Pages 11-35
The Relation Between Quantum Mechanics And Classical Mechanics: A Survey Of Some Mathematical Aspects....Pages 37-76
Lifshitz Singularity of the Integrated Density of States and Absence of Diffusion Near the Bottom of the Spectrum for A Random Hamiltonian....Pages 77-82
Fluctuations in Nuclear Spectra....Pages 83-101
Characterization of Fluctuations of Chaotic Quantum Spectra....Pages 103-111
Spectral Fluctuations and Chaos in Quantum Systems....Pages 113-122
Aspects of Degeneracy....Pages 123-140
Periodic Orbits and a Correlation Function for the Semiclassical Density of States....Pages 141-147
Mild Chaos....Pages 149-164
Regular and Irregular Energy Spectra....Pages 165-170
Stochastic Ionization of Bound Electrons....Pages 171-186
Quantum Diffusion Limitation at Excitation of Rydberg Atom in Variable Field....Pages 187-204
Quantum Chaos and Anderson Localization....Pages 205-216
Transition of a Coherent Classical Wave to Phase Incoherence....Pages 217-225
Chaos in Dissipative Quantum Systems....Pages 227-233
Semiclassical Quantization on Fragmented Tori....Pages 235-254
Quantum Ergodicity And Intensity Fluctuations....Pages 255-292
Aspects of Intramolecular Dynamics in Chemistry....Pages 293-298
Semiclassical Analysis of Regular and Irregular Modes of Quantum Coupled Oscillators....Pages 299-308
Quantum Chaos as Basis for Statistical Mechanics....Pages 309-319
Continual Observations in Quantum Mechanics....Pages 321-344
Classical Quantization: Two Possible Approaches....Pages 345-351
Quantum Chaos and the Theory of Measurement....Pages 353-361
Bohr’s “Phenomenon” and “Law Without Law”....Pages 363-378
Back Matter....Pages 379-380
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