Projects / Programmes
Applied mathematics, theoretical physics and intelligent systems
January 1, 2022
- December 31, 2027
| Code |
Science |
Field |
Subfield |
| 1.02.00 |
Natural sciences and mathematics |
Physics |
|
| 1.01.00 |
Natural sciences and mathematics |
Mathematics |
|
| Code |
Science |
Field |
| 1.03 |
Natural Sciences |
Physical sciences |
| 1.01 |
Natural Sciences |
Mathematics |
theoretical physics, mathematical physics, statistical physics, nonlinar dynamics, classical and quantum chaos, dynamical systems, high energy theory, quantum field theory, string theories, qunatum gravity, ordinary differential equations, 16th Hilbert problem
Data for the last 5 years (citations for the last 10 years) on
April 28, 2024;
A3 for period
2018-2022
| Database |
Linked records |
Citations |
Pure citations |
Average pure citations |
| WoS |
575 |
22,521 |
20,040 |
34.85 |
| Scopus |
570 |
21,856 |
19,329 |
33.91 |
Researchers (10)
Organisations (1)
Abstract
Our program encompasses three major fields of research in theoretical physics and mathematics: nonlinear dynamics of classical and quantum chaos (Robnik), quantum field theory, high energy physics theory, string theories, quantum gravity (Cvetič), and theory of ordinary differential equations with applications in dynamical systems (Romanovski). Robnik's main efforts cover the dynamics and statistical properties of the time-dependent linear and nonlinear 1D and 2D Hamilton systems, to some extent also dissipative systems, development of the linear and nonlinear WKB method, and topics in quantum chaos. The emphasis is on understanding the structure and statistical properteis of eigenstates in phase space (Wigner and Husimi functions), their localization properties and the statistical properties of the energy spectra. Cvetič's research concerns the broad field of string theories, especially F-Theory and quantum gravity, both with applications in the elementary particle physics, as well in the cosmological context, including the studies of stabilty, microscopics and mesoscopics of black holes. Romanovski's research comprises studies of dynamical systems, in praticular of polynomial ordinary differential equations in the plane, qualitative and quantitative description of the structure of the phase portraits, theory of bifurcations, questions related to the 16th Hilbert problem, introduction of many new methods to solve these problems, including advanced compuer algebra, algebraic methods and graph theory. The important applications encompass chemical reactions (chemical kinetics), problems in the population kinematics and dynamics in biology and applications in engineering sciences, especially regarding the stability analysis of systems. In recent times they introduce analogous methods in higher dimensional systems, which is also the subject of the proposed research.
Significance for science
Robnik: The proposed research will essentially contribute to the advancement of science in the nonlinear dynamics of classical and quantum chaos and will develop new tools and methods of mathematical physics to be applied to the physically important model systems, paradigmatic case studies and general theory. It will contribute to the understanding of the statistical properties of 1D and 2D time-dependent Hamilton systems. It will also reveal new characteristics of the classical and quantum parametric resonance in various linear systems, and to the understanding of the dynamics and its statistical behaviour in nonlinear systems. These studies have important applications not only in physics, mathematics and natural sciences in general, but also in engineering sciences and elsewhere. Our research in quantum chaos, properties of the solutions of the time-dependent and time-independent Schroedinger equation and their statistical properties will contribute to the theoretical studies in this field, and also in many important experimental applications, whereever we face problems from the point of view of wave chaos, not only in quantum mechanics of atoms, molecules and solid state systems, but also in electromagnetic systems, in acoustics, plasma waves, water waves, seismic waves etc. Cvetič: The proposed research efforts encompass broad thrusts in fundamental theory, ranging from nonperturbative gravitational physics in consistent theories of quantum gravity (String Theory) to leading efforts in constructions of String Theory vacua and the study of their physics implications. Cvetič is a world-leading researcher in theoretical high energy physics with a background and strong track record in basic theory (Superstring/F-theory, supergravity, and general relativity) as well as in phenomenology (particle physics implications of fundamental theory). The proposed research is in a leading position to bridge the gap between basic theory and the experimental consequences of these theories. The proposed research is poised to make leading contributions along the following important directions: (i) it will advance our understanding of the internal and quantum structure of black holes in fundamental theories of quantum gravity; (ii) It will make important contributions to the full landscape of physically viable particle physics Standard Models in fundamental theories of quantum gravity (String and F-theory); (iii) It will provide important constraints on quantum field theories in consistent quantum theories in diverse space-time dimensions, thus deriving specific constraints emerging from String Universality. Romanovski: His research will contribute to the development of the theory of dynamical systems in Slovenia by transferring the scientific knowledge between researchers working at different institutions in Slovenia and by the intensive collaboration with the well-established research groups working in the field of dynamical systems around the world. Although the planned research mainly involves knowledge from the theory of dynamical systems for the achievement of the research goals we need knowledge from different fields of mathematics, the theory of chemical reaction networks, computer science. Thus, close collaboration and exchange of the expertise between the researchers of the program and the scientists of the University of Maribor and other institutions in Slovenia and abroad are crucial. The participants of the program are involved in the pedagogical work at the university of Maribor, so they will bring new ideas and methods in the teaching process. The proposed research ties together important and rapidly developing fields of dynamical systems, computer algebra and the theory of biochemical networks. Thus, the obtained knowledge will be important not only for mathematical science development but also in applied and technical studies. In particular it can be used for creating computational platforms for the symbolic analysis of general biological and chemical reaction networks.
Significance for the country
We shall continue our tradition in organizing top-level scientific conferences both in theoretical physics and mathematics in our fields, as well as general physics meetings such as annual Christmas symposia of physicists (every year since 2002). So far Robnik has organized since 1993 more than 55 meetings, most of them on the world-top level. This includes 9 international world-top level summer schools and conferences Let's Face Chaos through Nonlinear Dynamics (1993-2014) in Maribor and their continuation in Como, Italy (Let's Face Complexity: New Bridges Between Physical and Social Sciences, Sept 2017), 16 Japan-Slovenia Seminars on Nonlinear Science in Maribor, and at various universities in Japan such as Waseda University Tokyo, Tokyo University, Tokyo Metropolitan University, Kyoto University, Osaka University, Osaka City University, Nara Women's University, also on one occasion at Novacella (2006), Italy. Robnik also is active in the European Academy of Sciences and Arts (member since November 2012), organizing world-top level conferences in collaboration with the president EASA Prof. Klaus Mainzer (TU Munich) and Prof. Willibald Plessas (University of Graz, Austria). On 6 March 2020 we held a top-level meeting in Salzburg New Directions in Natural Sciences: Complexity, Machine Learning and Algorithms, with 6 prominent speakers including the Nobel Prize Laureate (Chemistry, 2002) Prof. Kurt Wuethrich, ETH Zuerich. Also Prof. Mirjam Cvetič was among them. For 18 June 2021 we plan another EASA meeting (zoom) Trends of Quantum Computing, Challenges of a Revolutionary Technology for Europe. By organizing world-top scientific meetings we contribute essentially to the connectivity of Slovenian science in our fields with leading institutions and individuals world-wide. The research group jointly is active also in teaching as well as in educating young researchers, PhD students. By including them, and other students of physics and mathematics, in the conferences we contribute essentially to their introduction to the scientific communities in our fields of research, and to their promotion, thereby strengthening the development of science in Slovenia in the international framework.
