Ebook: Stochasticity and Quantum Chaos: Proceedings of the 3rd Max Born Symposium, Sobótka Castle, September 15–17, 1993
- Tags: Theoretical Mathematical and Computational Physics, Quantum Physics, Probability Theory and Stochastic Processes
- Series: Mathematics and Its Applications 317
- Year: 1995
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-2
The Quantal Fattening of Fractals....Pages 3-11
How and When Quantum Phenomena Become Real....Pages 13-29
Chaotic Dynamics in a Periodically Driven Anharmonic Oscillator....Pages 31-37
Coherent and Incoherent Dynamics in a Periodically Driven Bistable System....Pages 39-55
The Ehrenfest Theorem for Markov Diffusions....Pages 57-62
The Quantum State Diffusion Model, Asymptotic Solutions, Thermal Equilibrium and Heisenberg Picture....Pages 63-71
Stochastic Representation of Quantum Dynamics....Pages 73-90
Level Repulsion and Exceptional Points....Pages 91-98
Type-II Intermittency in the Presence of Additive and Multiplicative Noise....Pages 99-113
Aspects of Liouville Integrability in Quantum Mechanics....Pages 115-121
KAM Techniques for Time Dependent Quantum Systems....Pages 123-129
Dissipation and Noise in Quantum Mechanics....Pages 131-136
Irregular Scattering, Number Theory, and Statistical Mechanics....Pages 137-148
Band Random Matrices, Kicked Rotator and Disordered Systems....Pages 149-160
Robust Scarred States....Pages 161-176
The Quasiclassical Statistical Description of Quantum Dynamical Systems and Quantum Chaos....Pages 177-183
Quantum Measurement by Quantum Brain....Pages 185-194
Time Reversal and Gaussian Measures in Quantum Physics....Pages 195-207
Stochastic Resonance in Bistable Systems with Fluctuating Barriers....Pages 209-216
Back Matter....Pages 217-226
Content:
Front Matter....Pages i-2
The Quantal Fattening of Fractals....Pages 3-11
How and When Quantum Phenomena Become Real....Pages 13-29
Chaotic Dynamics in a Periodically Driven Anharmonic Oscillator....Pages 31-37
Coherent and Incoherent Dynamics in a Periodically Driven Bistable System....Pages 39-55
The Ehrenfest Theorem for Markov Diffusions....Pages 57-62
The Quantum State Diffusion Model, Asymptotic Solutions, Thermal Equilibrium and Heisenberg Picture....Pages 63-71
Stochastic Representation of Quantum Dynamics....Pages 73-90
Level Repulsion and Exceptional Points....Pages 91-98
Type-II Intermittency in the Presence of Additive and Multiplicative Noise....Pages 99-113
Aspects of Liouville Integrability in Quantum Mechanics....Pages 115-121
KAM Techniques for Time Dependent Quantum Systems....Pages 123-129
Dissipation and Noise in Quantum Mechanics....Pages 131-136
Irregular Scattering, Number Theory, and Statistical Mechanics....Pages 137-148
Band Random Matrices, Kicked Rotator and Disordered Systems....Pages 149-160
Robust Scarred States....Pages 161-176
The Quasiclassical Statistical Description of Quantum Dynamical Systems and Quantum Chaos....Pages 177-183
Quantum Measurement by Quantum Brain....Pages 185-194
Time Reversal and Gaussian Measures in Quantum Physics....Pages 195-207
Stochastic Resonance in Bistable Systems with Fluctuating Barriers....Pages 209-216
Back Matter....Pages 217-226
....