Projects / Programmes
Effects of localization and tunneling in quantum chaotic systems
| Code |
Science |
Field |
Subfield |
| 1.02.00 |
Natural sciences and mathematics |
Physics |
|
| Code |
Science |
Field |
| P190 |
Natural sciences and mathematics |
Mathematical and general theoretical physics, classical mechanics, quantum mechanics, relativity, gravitation, statistical physics, thermodynamics |
nonlinear dynamics, quantum chaos, semiclassical limit, localization, tunneling, random matrices
Researchers (3)
Organisations (1)
Abstract
Generic Hamilton systems have classical dynamics of the mixed type in the classical phase space, which means that they exhibit regular motion on invariant tori for certain initial conditions, and chaotic dynamics for complementary initial onditions.
In generic quantum chaotic Hamilton systems in the semiclassical limit applies the so-called Principle of uniform semiclassical condensation (PUSC) of Wignner functions of eigenstates, from which the so-called Berry-Robnik picture arises and the statistics of eigenenergies (energy spectra). In this limit of sufficiently small Planck constant the entire energy spectrum of a mixed type system can be described as statistically independent superposition of regular and chaotic spectral sequences. The so-called E(k,L) probabilities factorize for each partition of the number k.
If the effective Planck constant is not sufficiently small we see the effects of correlations between the regular and chaotic eiegenstates, due to tunneling, and at the same time also the effects of localization in the chaotic components. Our goal is to describe theoretically as generally as possible the effects of localization and tunneling, to perform extensive numerical experiments on some important dynamical systems, in particular the billiard systems, and to develop further random matrix models. Finally we shall analyse also the experimental data for various systems, in particular for the microwave resonators.
Significance for science
Research of Prof. M. Robnik with coworkers in the framework of this project in the field of classical and quantum chaos is on the theoretical side a basic research, which describes the behaviour of quantum systems, which are classically chaotic. This includes not only quantum systems like e.g. molecules, atoms, elementary particles, and the systems in solid and condensed matter, but also other systems, which are described by wave equations, e.g. the electromagnetic waves (microwaves in microwave resonators, optical laser microresonators), acoustic waves, elastic waves, surface waves of liquids, etc., and also
other technologically interesting mesoscopic and nano systems like e.g. quantum dots, graphene, etc. Our basic research contributes to the understanding of the basic properties of chaotic systems, like their time evolution, their stationary states, in the case of quantum mechanics the structure of eigenstates in configuration and in the phase space (Wigner functions of the eigenstates), statistical properties of the eigenstates and of the energy spectra.
Significance for the country
In the field of theoretical physics of classical and quantum chaotic systems we deal with problems of chaotic wave systems, which have applications in many branches of applied physics, and even in engineering and technologies. In Slovenia this field has evolved since 1990s, when Prof. M. Robnik has founded and since then further developed the Center for Applied Mathematics and Theoretical Physics (CAMTP) at the University of Maribor. From there a series of new PhD students and postdocs from Slovenia and abroad has emerged. Some of them have meanwhile developed their own research groups. For example, Prof.T. Prosen at the Faculty of Mathematics and Physics of the University of Ljubljana, Prof. G. Veble became the head of the Research and Development Center of the prestigeous company Pipistrel d.o.o. in Ajdovščina, where his experience in nonlinear dynamics is very useful, and he also does research at the University of Nova Gorica. Others did very well as well, like e.g. Prof. Baowen Li, who was a postdoctoral coworker of Prof. Robnik, and became a full professor at the National University of Singapore, where he founded a large, extremely successful and worldwide known research group in the field of nonlinear dynamics and some other fields of theoretical physics. Last but not least we have to emphasize that CAMTP organizes every year a three-days symposium on physics (Symposium of the Physicists of the University of Maribor, s.c. Christmas Symposium), which connects all Slovenian physicists, every year, since 2002. Young physicists have the opportunity to present their work, the experienced researchers exchange most recent information of scientific and academic nature, in addition to their invited lectures. Every year we have also some very distinguished guests, invited speakers and lecturers from abroad. Furthermore, CAMTP organizes every three years the international Summer School and Conference "Let's Face Chaos through Nonlinear Dynamics", so far we had 7, the 8th one will take place on 26 June - 10 July 2011, which is each time a worldwide top meeting on nonlinear dynamics. CAMTP also organizes one-day mini symposia on physics, and the institute seminars with guest speakers from Slovenia and from abroad.
Apart from that it also educates doctoral students from Slovenia and abroad, currently 4 (2 from Slovenia, 1 from Greece and 1 from Brazil). In this respect CAMTP contributes quite essentially to the development and promotion of the Slovenian science in the world, and at the same time brings new knowledge to the Slovenian science. By means of popular articles and interviews (in the daily newspaper Večer) CAMTP contributes also to the promotion of physics, mathematics and astronomy in Slovenia.
Most important scientific results
Annual report
2008,
2009,
final report,
complete report on dLib.si
Most important socioeconomically and culturally relevant results
Annual report
2008,
2009,
final report,
complete report on dLib.si
