Projects / Programmes
Applied Mathematics, Theoretical Physics and Intelligent Systems
January 1, 2015
- December 31, 2021
| Code |
Science |
Field |
Subfield |
| 1.02.00 |
Natural sciences and mathematics |
Physics |
|
| 1.01.00 |
Natural sciences and mathematics |
Mathematics |
|
| Code |
Science |
Field |
| P190 |
Natural sciences and mathematics |
Mathematical and general theoretical physics, classical mechanics, quantum mechanics, relativity, gravitation, statistical physics, thermodynamics |
| Code |
Science |
Field |
| 1.03 |
Natural Sciences |
Physical sciences |
Nonlinear dynamics, classical and quantum chaos, Hamiltonian and disspative autonomous and nonautonomous dynamical systems, statistical phys., ordinary differential equations, limit cycles, bifurcations, Hilbert's 16th problem, string theory, high energy theory, gravitational physics, black holes
Researchers (9)
Organisations (1)
Abstract
The finishing research program 2009-2014 has been carried out very successfully. This claim is strongly supported by the fact that the program team has collectively about 18.000 citations and published 89 papers in the past 5 years. Individually: Robnik 17, Romanovski 40, Cvetič 32; citations: Robnik 3500, Cvetič 15.000, Romanovski 300. H-index: Robnik about 30, Romanovski about 10, Cvetič about 71. In the framework of the research program we shall continue researching in the field of nonlinear dynamics, i.e. the theory of classical and quantum chaos, studying ordinary differential equations and dynamical systems, and performing theoretical research in the string theory, their compactifications, gravitational physics and connections with the theory of elementary particles. Robnik shall direct his work towards time-dependent classical and quantum dynamical systems, in particular in the study of their statistical properties within the statistical mechanics in the sense of Gibbs. In the quantum chaos we are interested primarily in the mixed-type systems, where the Berry-Robnik theory applies, which is generalized to include the quantum localization of the chaotic eigenstates. Important paradigmatic systems are billiard systems, in particular the s.c. Robnik billiard.
Romanovski intends to investigate in depth the interrelation of normal forms, Lyapunov functions, center manifolds, different kinds of symmetries and integrability of two-dimensional and higher-dimensional systems of autonomous ordinary differential equations and on this basis to develop algorithms for deciding on stability of systems, description of bifurcations and construction of integrals in a closed form. He will continue his collaborations with many coworkers worldwide, also in the interdisciplinary sense (theoretical physics and theoretical chemistry). Cvetič plans projects with implications both in the gravitational physics as well as in the physics of elementary particles, both stemming from the fundamental theory. Her research plans will be directed in the black holes in the string theory, where she has already made seminal contributions. Cvetič also plans to systematically explore particle physics implications of consistent string compactifications with D-branes. With the start-up of the LHC, such studies are important as they address within this corner of the landscape which particles beyond the MSSM (Minimal Supersymmetric Standard Model) are preferred by stringy consistency conditions. Cvetič is the worldwide leading expert in this field and has collaborations with numerous researchers worldwide.
Significance for science
Marko Robnik: We believe that our studies of the low-dimensional, even one-dimensional,
time-dependent Hamiltonian systems and their statistical properties are fundamental in the context of statistical mechanics in the sense of Gibbs.We show under what conditions are the
changes of non-autonomous systems irreversible in the mean (the entropy of Gibbs increases). Furthermore, our studies elucidate under what conditions the Fermi acceleration (i.e. the unbounded growth of the energy) is possible, classically and quantum mechanically. Our studies in quantum chaos bring new understanding of the role and consequences of the important phenomenon of the quantum dynamical localization of chaotic eigenstates. These results will have important consequences in describing and understanding generic classical and quantal autonomous and non-autonomous Hamiltonian systems with many applications in all branches of physics. In the form of a series of seminar lectures (Diploma seminar) for the students of physics at FNM UM we transfer these new findings in the pedagogical process to the new generation of physicists. We also educate PhD students in research and in the regular lecture courses and in other meetings (Summer Schools, Christmas Symposia, Spring Schools on Physics, Japan-Slovenia Seminars, Socrates Workshops).
Valery Romanovski: The study will contribute to the further development of the theory of dynamical systems, in particular, to the understanding of bifurcations in such systems. This is important for various applied and technical sciences because it helps to determine stable regimes of the system and control the behavior of the system. Since most dynamical systems are described using partial and ordinary differential equations our studies on the qualitative theory of differential equation, theory of integrability and theory of stability will bring new theoretical knowledge and will help understand deeply the behavior of dynamical systems. The obtained knowledge will also help understand better the dynamics of biological and chemical processes and this can be helpful for research in this field at the research and development departments of Slovenian companies dealing with such studies. Our research will also contribute to the transfer of knowledge to pedagogical sphere, since we are included in the pedagogical work at Slovenian universities.
Mirjam Cvetič: The efforts are at the forefront of theoretical high energy physics, addressing fundamental questions of gravitational physics (black holes in string theory) and particle physics implications (string compactification). These efforts contribute to the conceptual insights into the microscopic origin of black holes, such as the black hole entropy. In particular the efforts to explore the microscopic structure of the non-extremal black holes can potentially have important impact for the microscopic origin of astrophysical black holes. On the other hand the string compactification program, which is one of the leading world efforts, contributes to the cutting edge developments both in string theory and in mathematics. In particular, the geometric analysis of the singularities and their resolutions for Calabi-Yau spaces within F-theory contributes to fundamental insights into large classes of string compactifications, and thus provides broad exploration of particle physics implications of string theory.
Significance for the country
The research program P1-0306 Applied Mathematics, Theoretical Physics and Intelligent Systems is the core of funding CAMTP - Center for Applied Mathematics and Theoretical Physics of the University of Maribor. CAMTP is one of the very few scientific research institutes in Maribor in general, and the only one in the field of natural sciences and mathematics. It is exceptionally active, as in addition to the research work it carries out activities in the pedagogical/educational processes and organizes scientific conferences and other meetings. Marko Robnik lectures within the Diploma seminar to the students of physics at FNM UM (Faculty of Natural Sciences and Mathematics of the University of Maribor), and also within the MPŠ JS (International Graduate School Jožef Stefan in Ljubljana), Valery Romanovski delivers regular lectures for the students of mathematics at FNM UM, Mirjam Cvetič lectures at the International Spring Schools in Physics in Maribor. The conference activities: CAMTP organizes 2-3 scientific meetings per year. Since 1993 there are in total about 48. This are seven series of scientific meetings: International Summer Schools, Christmas Symposiums, Japan-Slovenia Seminars, European Advanced Studies Conferences, Socrates Workshops, Computer Algebra and Scientific Computing, and Out of the Box Conferences. Of course, we also educate a number of excellent young researchers and other PhD students. Also, there are strong international connections and collaborations, in the form of bilateral projects (USA, Russia, China, Turkey), in the form of European Projects (V. Romanovski) and through the connections of Prof. Mirjam Cvetič with oustanding and distinguished coworkers from all over the world. According to the financial support and the efficiency per one researcher, CAMTP is certainly one of the most active and efficient research institutes in Slovenia as well as in the international area. Some of the former PhD students of Prof. M. Robnik are successful in academic and research community and in the industry: Prof. Dr. Tomaž Prosen (1995), Full Professor at the FMF of the University of Ljubljana, recipient of the Zois Award (2005), which is the highest award for science in Slovenia, winner of the Bessel Prize (Germany), one of the most visible theoretical physicists of his generation worldwide; Prof. Dr. Gregor Veble (2001), associate professor at the University of Nova Gorica and head of the R&D laboratory of the Pipistrel company (Ajdovščina), recipient of the Puh Award (the highest award for technological achievements in the Republic of Slovenia), and the main developer of the ultra light airplanes, which won twice the NASA competitions in the USA. For its existence CAMTP needs at least three FTEs within the research program. We are convinced that the mission and all the activities of the CAMTP are quite an essential contribution towards the scientific, cultural and technological development of Slovenia, especially in the Maribor area. This fact is strongly supported by the fact that the research program group has collectively about 18.000 citations and published in the last five years 89 original papers. Individually: Robnik 17, Romanovski 40, Cvetič 32; citations: Robnik 3500, Cvetič 15.000, Romanovski 300. H-index: Robnik about 30, Romanovski about 10, Cvetič about 71. The past socio-economical and cultural achievements are listed in section 14., and of course we shall intensively continue these activities.
Most important scientific results
Annual report
2015,
interim report
Most important socioeconomically and culturally relevant results
Annual report
2015,
interim report
