This volume covers a wide range of problems in the quantum mechanics of non-integrable systems, presented by experts in the field. The main part of the work concerns quantum chaos and dynamical aspects of chaos in particular. Among the subjects which are treated are: periodic perturbations, small denominators in quantum mechanics, tunnelling in the presence of a periodic perturbation, chaotic scattering, quantum maps, level statistics of chaotic systems and random matrices. The papers are concerned with mathematically rigorous derivations of results, as well as with their physical applications, such as scattering, ionization and tunnelling. The papers discuss recent results which have not been published in book form before. All contributors present new methods to approach quantum chaos rather than extending conventional techniques. This book is intended for specialists in the field of dynamical systems, quantum mechanics and stochastic processes. It can also serve as an introduction to graduate and postgraduate students of theoretical physics and mathematics.

The XII Max Born Symposium has a special character. It was held in honour th of Jan Lopusza nski on the occasion of his 75 birthday. As a rule the Max Born Symposia organized by the Institute of Theoretical Physics at the University of Wroc law were devoted to well-de ned subjects of contemporary interest. This time, however, the organizers decided to make an exception. Lopusza nski’s in?uence on and contribution to the development of th- retical physics at Wrocla w University is highly appreciable. His personality and scienti c achievements gave him authority which he used to the best - vantage of the Institute. In fact we still pro t from his knowledge, experience and judgment. Lopusza nski’s scienti c activity extended over about half a century. He successfully participated in research on the most important and fascinating issues of theoretical physics. During his scienti c career he met and made friends with many outstanding physicists who shaped theoretical physics to the present form. For this reason, as well as the coincidence of the approaching end of the century, we thought that it would be interesting and instructive to give the symposium a retrospective character. We decided to trust the speakers’ judgment and intuition for the choice of subjects for their talks. We just asked them to give the audience the important message based on their knowledge and experience.

The XII Max Born Symposium has a special character. It was held in honour th of Jan Lopusza nski on the occasion of his 75 birthday. As a rule the Max Born Symposia organized by the Institute of Theoretical Physics at the University of Wroc law were devoted to well-de ned subjects of contemporary interest. This time, however, the organizers decided to make an exception. Lopusza nski’s in?uence on and contribution to the development of th- retical physics at Wrocla w University is highly appreciable. His personality and scienti c achievements gave him authority which he used to the best - vantage of the Institute. In fact we still pro t from his knowledge, experience and judgment. Lopusza nski’s scienti c activity extended over about half a century. He successfully participated in research on the most important and fascinating issues of theoretical physics. During his scienti c career he met and made friends with many outstanding physicists who shaped theoretical physics to the present form. For this reason, as well as the coincidence of the approaching end of the century, we thought that it would be interesting and instructive to give the symposium a retrospective character. We decided to trust the speakers’ judgment and intuition for the choice of subjects for their talks. We just asked them to give the audience the important message based on their knowledge and experience.

The XII Max Born Symposium has a special character. It was held in honour th of Jan Lopusza nski on the occasion of his 75 birthday. As a rule the Max Born Symposia organized by the Institute of Theoretical Physics at the University of Wroc law were devoted to well-de ned subjects of contemporary interest. This time, however, the organizers decided to make an exception. Lopusza nski’s in?uence on and contribution to the development of th- retical physics at Wrocla w University is highly appreciable. His personality and scienti c achievements gave him authority which he used to the best - vantage of the Institute. In fact we still pro t from his knowledge, experience and judgment. Lopusza nski’s scienti c activity extended over about half a century. He successfully participated in research on the most important and fascinating issues of theoretical physics. During his scienti c career he met and made friends with many outstanding physicists who shaped theoretical physics to the present form. For this reason, as well as the coincidence of the approaching end of the century, we thought that it would be interesting and instructive to give the symposium a retrospective character. We decided to trust the speakers’ judgment and intuition for the choice of subjects for their talks. We just asked them to give the audience the important message based on their knowledge and experience.

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.

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.

This volume covers a wide range of problems in the quantum mechanics of non-integrable systems, presented by experts in the field. The main part of the work concerns quantum chaos and dynamical aspects of chaos in particular. Among the subjects which are treated are: periodic perturbations, small denominators in quantum mechanics, tunnelling in the presence of a periodic perturbation, chaotic scattering, quantum maps, level statistics of chaotic systems and random matrices. The papers are concerned with mathematically rigorous derivations of results, as well as with their physical applications, such as scattering, ionization and tunnelling. The papers discuss recent results which have not been published in book form before. All contributors present new methods to approach quantum chaos rather than extending conventional techniques. This book is intended for specialists in the field of dynamical systems, quantum mechanics and stochastic processes. It can also serve as an introduction to graduate and postgraduate students of theoretical physics and mathematics.

The XII Max Born Symposium has a special character. It was held in honour th of Jan Lopusza nski on the occasion of his 75 birthday. As a rule the Max Born Symposia organized by the Institute of Theoretical Physics at the University of Wroc law were devoted to well-de ned subjects of contemporary interest. This time, however, the organizers decided to make an exception. Lopusza nski’s in?uence on and contribution to the development of th- retical physics at Wrocla w University is highly appreciable. His personality and scienti c achievements gave him authority which he used to the best - vantage of the Institute. In fact we still pro t from his knowledge, experience and judgment. Lopusza nski’s scienti c activity extended over about half a century. He successfully participated in research on the most important and fascinating issues of theoretical physics. During his scienti c career he met and made friends with many outstanding physicists who shaped theoretical physics to the present form. For this reason, as well as the coincidence of the approaching end of the century, we thought that it would be interesting and instructive to give the symposium a retrospective character. We decided to trust the speakers’ judgment and intuition for the choice of subjects for their talks. We just asked them to give the audience the important message based on their knowledge and experience.

The XII Max Born Symposium has a special character. It was held in honour th of Jan Lopusza nski on the occasion of his 75 birthday. As a rule the Max Born Symposia organized by the Institute of Theoretical Physics at the University of Wroc law were devoted to well-de ned subjects of contemporary interest. This time, however, the organizers decided to make an exception. Lopusza nski’s in?uence on and contribution to the development of th- retical physics at Wrocla w University is highly appreciable. His personality and scienti c achievements gave him authority which he used to the best - vantage of the Institute. In fact we still pro t from his knowledge, experience and judgment. Lopusza nski’s scienti c activity extended over about half a century. He successfully participated in research on the most important and fascinating issues of theoretical physics. During his scienti c career he met and made friends with many outstanding physicists who shaped theoretical physics to the present form. For this reason, as well as the coincidence of the approaching end of the century, we thought that it would be interesting and instructive to give the symposium a retrospective character. We decided to trust the speakers’ judgment and intuition for the choice of subjects for their talks. We just asked them to give the audience the important message based on their knowledge and experience.

The XII Max Born Symposium has a special character. It was held in honour th of Jan Lopusza nski on the occasion of his 75 birthday. As a rule the Max Born Symposia organized by the Institute of Theoretical Physics at the University of Wroc law were devoted to well-de ned subjects of contemporary interest. This time, however, the organizers decided to make an exception. Lopusza nski’s in?uence on and contribution to the development of th- retical physics at Wrocla w University is highly appreciable. His personality and scienti c achievements gave him authority which he used to the best - vantage of the Institute. In fact we still pro t from his knowledge, experience and judgment. Lopusza nski’s scienti c activity extended over about half a century. He successfully participated in research on the most important and fascinating issues of theoretical physics. During his scienti c career he met and made friends with many outstanding physicists who shaped theoretical physics to the present form. For this reason, as well as the coincidence of the approaching end of the century, we thought that it would be interesting and instructive to give the symposium a retrospective character. We decided to trust the speakers’ judgment and intuition for the choice of subjects for their talks. We just asked them to give the audience the important message based on their knowledge and experience.

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.

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.