Projects / Programmes
Quantum chaos in chaotic mixed type systems
| Code |
Science |
Field |
Subfield |
| 1.02.02 |
Natural sciences and mathematics |
Physics |
Theoretical physics |
| Code |
Science |
Field |
| P002 |
Natural sciences and mathematics |
Physics |
| Code |
Science |
Field |
| 1.03 |
Natural Sciences |
Physical sciences |
nonlinear dynamics, classical and quantum chaos, Hamilton systems, systems of the mixed type, energy spectra, eigenstates, Wigner functions, applications in mesoscopic and nano systems
Researchers (4)
Organisations (2)
Abstract
Quantum chaos deals with the aspects of quantum or other wave systems, which are analogy and manifestation of the phenomena of classical chaos in Hamiltonian systems. Such systems can be in extreme case integrable (regular and stable), or fully chaotic (ergodic), or somewhere in between, of the mixed type (partially chaotic, for some initial conditions in the phase space, and regular for other complementary initial conditions in the phase space). Just the mixed type systems are, first, most typical and abundant, and second, at the same time most complex and their analysis is very difficult. Our project will be devoted to the problems of the mixed type. We are interested in the properties of the solutions of the Schroedinger equation for such systems, namely the structure of the wave functions and Wigner functions of the eigenstates, of the energy spectra and their statistical properties, and also the processes of the so called dynamical tunneling. The methods of research are the exact numerical solving of the Schroedinger equation, as well as the application of the semiclassical methods, analysis of various model systems and ensembles of random matrices, and researching of the relevant phenomena in the classical Hamilton chaos. We are interested in model systems in one dimension (time periodic Floquet systems), in two and higher dimensions. The beginning of this research goes back to 1984, when Robnik published a paper on the spectral statistics in the mixed type regime of a billiard (so called Robnik billiard, 1983), and when Berry and Robnik (1984) published the first paper on the semiclassical theory of level spacings, the so called Berry-Robnik theory, which is exact in the limit of sufficiently small effective Planck constant. Since then the topics has developed very intensively, in particular in the years 1990-2000 (T. Prosen and M. Robnik), and worldwide, most recently in collaboration with B. Batistić (2010). Many groups worldwide have treated these problems which are still very hot topic. We should mention the work at the University of Marburg (Prof. H.-J. Stoeckmann), where also the experiments with the microwave resonators are performed, and also the work of the group in Dresden (Prof. R. Ketzmerick and coworkers) and of the group at TU in Vienna (Prof. J. Burgdoerfer) and other groups all over the world, which also deal with theory and applications in quantum dots, microoptical cavities and other mesoscopic and nano systems. On the theoretical side, using the Gutzwiller theory, the group of Prof. F. Haake (Essen) succeeded to prove the s.c. Bohigas, Giannoni and Schmit conjecture, namely that the statistics of fully chaotic systems is equivalent to the theory of the Gaussian ensembles of random matrices (RMT). Berry, Keating and Schomerus and others have studied semiclassical properties in the mixed regime, also taking into account the bifurcations of classical periodic orbits. In the mixed regime we have developed approaches to reconstruct the quantum states and investigated the consequences of the principle of uniform semiclassical condensation of the Wigner functions (G. Veble and M. Robnik 1997-2001). In most recent time a lot of attention has been paid to the effects of localization and tunneling, which at the larger values of the effective Planck constant lead to the deviation of the chaotic states and their statistical properties from the Berry-Robnik statistics (Batistić and Robnik 2010). We have shown that the localization phenomena can survive up to much larger energies (by several orders of magnitude) than predicted by the qualitative theory of dynamical localization. We shall study these phenomena more deeply theoretically and test the theory in quantum model systems, and develop semiclassical theory of known empirical and semiempirical findings. We shall perform experiments with microwave resonators (Prof. H.-J. Stoeckmann), who is the leader and the first worldwide to perform such experime
Significance for science
Our findings and results contribute to the wealth of knowledge in the basic research in the field of theoretical physics, namely in the field of nonlinear dynamics, dynamical systems and classical and quantum chaos. In the period 2011-2014 we have published jointly 10 extensive important original papers in renowned international journals, the impact of our works is mirrored in our joint cumulative number of citations, which is about 4000. All above listed members of the research project group have a great number of invited plenary lectures at renowned international conferences and universities and institutes all around the world. In addition, CAMTP organizes even seven series of scientific meetings, almost all of them are internationally and worldwide top meetings, which contributes to the dissemination of scientific information, education of young scientists and stimulations of new scientific ideas, paradigms and collaborations in the world. We carry out the following seven series of scientific meetings: (1) International summer schools and conferences Let's Face Chaos through Nonlinear Dynamics, (2) Christmas symposia of physicists, (3) Japan-Slovenia Seminars, (4) SOCRATES Workshops, (5) European Advanced Studies Conferences, (6) Dynamical systems and symbolic computation, and (7) Out of the Box Conferences. In the latter one (May 2012) we had among the 30 invited speakers 3 Nobel Prize Winners. In doing so we pay special attention to the development and maintaining of excellent scientific contacts and collaborations with the colleagues in the neighbouring countries of our international area, namely in Austria, Hungary, Italy and Croatia, and in the broader area in particular in Germany and Japan, China, USA and Russia.
Significance for the country
The findings and results of our research program contribute not only to the worldwide wealth of knowledge, but enrich the scientific work in Slovenia on the highest level. With the exception of the research group of Prof. Tomaž Prosen at the Faculty of Mathematics and Physics of the University of Ljubljana (FMF UL), which however nicely complements our research activities, there are practically no other researchers in Slovenia in this field of science. The level of our work is evident from the data that we jointly have about 240 original papers and about 4000 citations, h-index about 30 (MR), 15 (VR). In addition we successfully educate young researchers and other PhD students both at FMF UL and at the Faculty of Natural Sciences and Mathematics of the University of Maribor (FNM UM) (so far we had 8 awarded PhD degrees) and take part in the pedagogical process of FNM UM in physics and mathematics at all three stages of the Bologna system. We educate also postdoctoral students from Slovenia and abroad. The foreign researchers, who return to foreign countries, play the role of the ambassadors of the Slovenian science in the world. Furthermore, we are exceptionally active in organizing the elitist national and international meetings. Since 1993 we have organized more than 50 conferences, per year even 2-4 conferences, mainly in the field of physics, some in the field of mathematics (so far 3). We carry out seven series of scientific meetings: (1) International summer schools and conferences Let's Face Chaos through Nonlinear Dynamics, (2) Christmas symposia of physicists, (3) Japan-Slovenia Seminars, (4) SOCRATES Workshops, (5) European Advanced Studies Conferences, (6) Dynamical systems and symbolic computation, and (7) Out of the Box Conferences. In the latter one (May 2012) we had among the eminent internationally renowned 30 invited speakers 3 Nobel Prize Winners. In doing so we pay special attention to the development and maintaining of excellent scientific contacts and collaborations with the colleagues in the neighbouring countries of our international area, namely in Austria, Hungary, Italy and Croatia, and in the broader area in particular in Germany and Japan, China, USA and Russia. All this contributes in an essential way to the promotion of Slovenian science abroad, in fact in the entire world.
Most important scientific results
Annual report
2011,
2012,
2013,
final report,
complete report on dLib.si
Most important socioeconomically and culturally relevant results
Annual report
2011,
2012,
2013,
final report,
complete report on dLib.si
