Stochasticity and Quantum Chaos

1. Front Matter

   Pages i-2

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2. The Quantal Fattening of Fractals

   • N. L. Balazs

   Pages 3-11

3. How and When Quantum Phenomena Become Real

   • Ph. Blanchard, A. Jadczyk

   Pages 13-29

4. Chaotic Dynamics in a Periodically Driven Anharmonic Oscillator

   • Yu. L. Bolotin, V. Yu. Gonchar, M. Ya. Granovsky

   Pages 31-37

5. Coherent and Incoherent Dynamics in a Periodically Driven Bistable System

   • T. Dittrich, F. Grossmann, P. Hänggi, B. Oelschlägel, R. Utermann

   Pages 39-55

6. The Ehrenfest Theorem for Markov Diffusions

   • P. Garbaczewski

   Pages 57-62

7. The Quantum State Diffusion Model, Asymptotic Solutions, Thermal Equilibrium and Heisenberg Picture

   • N. Gisin

   Pages 63-71

8. Stochastic Representation of Quantum Dynamics

   • Z. Haba

   Pages 73-90

9. Level Repulsion and Exceptional Points

   • W. D. Heiss, W.-H. Steeb

   Pages 91-98

10. Type-II Intermittency in the Presence of Additive and Multiplicative Noise

    • H. Herzel, F. Argoul, A. Arneodo

    Pages 99-113

11. Aspects of Liouville Integrability in Quantum Mechanics

    • J. Hietarinta

    Pages 115-121

12. KAM Techniques for Time Dependent Quantum Systems

    • H. R. Jauslin

    Pages 123-129

13. Dissipation and Noise in Quantum Mechanics

    • N. G. Van Kampen

    Pages 131-136

14. Irregular Scattering, Number Theory, and Statistical Mechanics

    • Andreas Knauf

    Pages 137-148

15. Band Random Matrices, Kicked Rotator and Disordered Systems

    • Luca Molinari

    Pages 149-160

16. Robust Scarred States

    • D. Richards

    Pages 161-176

17. The Quasiclassical Statistical Description of Quantum Dynamical Systems and Quantum Chaos

    • Yu. P. Virchenko

    Pages 177-183

18. Quantum Measurement by Quantum Brain

    • Mari Jibu, Kunio Yasue

    Pages 185-194

19. Time Reversal and Gaussian Measures in Quantum Physics

    • J. C. Zambrini

    Pages 195-207

20. Stochastic Resonance in Bistable Systems with Fluctuating Barriers

    • L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta, S. Santucci

    Pages 209-216

These are the proceedings of the Third Max Born Symposium which took place at SobOtka Castle in September 1993. The Symposium is organized annually by the Institute of Theoretical Physics of the University of Wroclaw. Max Born was a student and later on an assistant at the University of Wroclaw (Wroclaw belonged to Germany at this time and was called Breslau). The topic of the Max Born Sympo­ sium varies each year reflecting the developement of theoretical physics. The subject of this Symposium "Stochasticity and quantum chaos" may well be considered as a continuation of the research interest of Max Born. Recall that Born treats his "Lectures on the mechanics of the atom" (published in 1925) as a nrst volume of a complete monograph (supposedly to be written by another person). His lectures concern the quantum mechanics of integrable systems. The quantum mechanics of non-integrable systems was the subject of the Third Max Born Symposium. It is known that classical non-integrable Hamiltonian systems show a chaotic behaviour. On the other hand quantum systems bounded in space are quasiperi­ odic. We believe that quantum systems have a reasonable classical limit. It is not clear how to reconcile the seemingly regular behaviour of quantum systems with the possible chaotic properties of their classical counterparts. The quantum proper­ ties of classically chaotic systems constitute the main subject of these Proceedings. Other topics discussed are: the quantum mechanics of dissipative systems, quantum measurement theory, the role of noise in classical and quantum systems.

• Gaussian measure
• Stochastic processes
• Theoretical physics
• quantum chaos
• quantum mechanics
• statistics
• stochastic process

• Institute of Theoretical Physics, University of Wrocław, Wrocław, Poland

  Zbigniew Haba, Wojciech Cegła, Lech Jakóbczyk

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