Order,Disorder and Chaos in Quantum Systems

1. Point and Contact Interactions, Self-Adjoint Extensions

   1. Green’s Function for the Aharonov-Bohm Effect with a Non-Abelian Gauge Group

      • Pavel Šťovíček

      Pages 183-193

   2. A Model of Zero-Width Slits and the Real Diffraction Problem

      • I. Yu. Popov

      Pages 195-196

   3. Construction of an Inelastic Scatterer in Nanoelectronics by the Extension-Theory Methods

      • I. Yu. Popov

      Pages 197-198

   4. On Boundary Theory for Schrödinger Operators and Stochastic Processes

      • J. F. Brasche, W. Karwowski

      Pages 199-208

   5. Dirac Hamiltonian with Coulomb Potential and Contact Interaction on a Sphere

      • J. Dittrich, P. Exner, P. Šeba

      Pages 209-219

   6. Self-Adjoint Extensions of Schroedinger Operators with Singular Potentials

      • A. N. Kochubei

      Pages 221-227

   7. Currents and the Extensions Theory

      • Yu. A. Kuperin, E. A. Yarevsky

      Pages 229-233

2. Quantum Chaos

   1. Front Matter

      Pages 235-235

      PDF

   2. Chaotic Quantum Billiards

      • Petr Šeba

      Pages 237-258

   3. Relevance of the Localization to Quasienergy Statistics in Quantum Chaotic Systems

      • F. M. Izrailev

      Pages 259-277

   4. Singular Continuous Quasi-Energy Spectrum in the Kicked Rotator with Separable Perturbation: Onset of Quantum Chaos?

      • B. Milek, P. Šeba

      Pages 279-299

   5. Relation between Correlation Functions and Spectrum Statistics in the Region of Quantum Chaos

      • G. P. Berman, F. M. Izrailev

      Pages 301-304

3. Other Topics

   1. Front Matter

      Pages 305-305

      PDF

   2. Localization Effects in Non-Homogeneous Dielectrics

      • P. B. Kurasov, B. S. Pavlov

      Pages 307-313

   3. A Self-Adjoint Dilation of the Linear Boltzmann Operator

      • Yu. A. Kuperin

      Pages 315-318

   4. Kato Problem for Functional-Differential Equations and Difference Schrödinger Operators

      • G. A. Derfel

      Pages 319-321

   5. An Existence Theorem for Some Nonlinear Nonlocal Schroedinger Operators and the Soliton-Like Solutions for the Corresponding Dynamic Systems

      • S. I. Petrukhnovsky

      Pages 323-326

   6. The Sturm-Liouville Problem with a Potential Linear in Spectral Parameter

      • V. N. Pivovarchik

      Pages 327-329

   7. Stochastic Model of Tree Growth

      • M. A. Antonets, I. A. Shereshevsky

      Pages 331-334

   8. Critical Phenomenon in the Stationary Model of Random Growth

      • M. A. Antonets, I. A. Shereshevsky

      Pages 335-338

The present volume collects the contributions to the conference "Order, disorder and chaos in quantum systems" which was held at Dubna last October. It is the third meeting in the series started three years ago in which we tried to put together mathematical physicists from the member and non-member countries of JINR with their colleagues from soviet universities and institutes using this international centre as a convenient basis. As in the previous cases, new faces, subj ects and ideas appeared but the spirit remained the same, relaxed and inspirative. Among this conference contributions, a majority should be listed in the "orderly" category. Being more specific, this means mostly various aspects of the theory of Schroedinger operators that has been always a core of quantum mechanics. In spite of the fact that it is studied already for several decades, there are still many interesting problems to solve as some of the lectures collected below witness. At the same time, the theory extends to some new areas motivated by physical problems ; let us mention Schroedinger operators in complicated spatial domains appearing in some parts of solid-state physics or various models using the concept of contact interactions. Our world is far from perfect and to keep a perfect order is difficult not only in everyday life but also in most physical systems. Theoreticians are used to take this fact into account introducing stochastic factors into their considerations.

• Invariant
• Mathematica
• approximation
• chaos
• differential equation
• equation
• function
• growth
• mechanics
• perturbation
• perturbation theory
• statistics
• symmetric relation
• system
• theorem

• Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Môscow, USSR

  Pavel Exner, Hagen Neidhardt

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