Projects / Programmes
January 1, 2019
- December 31, 2027
| Code |
Science |
Field |
Subfield |
| 1.01.00 |
Natural sciences and mathematics |
Mathematics |
|
| 1.02.02 |
Natural sciences and mathematics |
Physics |
Theoretical physics |
| 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 |
| 1.01 |
Natural Sciences |
Mathematics |
| 1.03 |
Natural Sciences |
Physical sciences |
Integrability, Manybody chaos, Statistical mechanics, Nonequilibrium, Transport, Exact solutions, Many body localization, KAM theorem, Universality, Dynamical systems, Markov chains
Data for the last 5 years (citations for the last 10 years) on
April 22, 2024;
A3 for period
2018-2022
| Database |
Linked records |
Citations |
Pure citations |
Average pure citations |
| WoS |
446 |
16,765 |
14,508 |
32.53 |
| Scopus |
448 |
17,617 |
15,292 |
34.13 |
Researchers (17)
Organisations (1)
Abstract
The derivation of macroscopic equations such as the diffusion equation and hydrodynamics from the microscopic Hamiltonian (or Schroedinger) dynamics governing the motion of the atomic constituents of matter is one of the central unsolved problems of nonequilibrium statistical mechanics. Within this research programme we shall strive to find exact, explicit and rigorous results in this direction in particular simple models of interacting systems in low dimensions, both classical and quantum. We aim at identifying universality classes of nonequilibrium behaviour and identify exactly solvable models within most important universality classes. We believe this would not only be possible among the so-called integrable systems, but also among strongly chaotic systems, where our goal is to find exactly solvable models of many-body quantum chaos and understand deep connections between dynamics and random matrix theory.
While one typically associates integrability with translationally invariant systems, which will be one of the main focuses of the programme, one can also get an effective integrable system in the presence of strong disorder. Physics of disordered systems is therefore interesting from several fundamental perspectives: (i) for weak disorder one might be interested in the stability of clean (integrable) systems -- e.g., an existence of any KAM-like theorem for quantum many-body systems, (ii) for strong disorder one can in some cases again approach an "integrable" limit, namely that of a many-body localized system. Both integrable limits can be studied using tools of mathematical physics, like rigorous perturbation theory, or even exact calculations. While the field of studying weak-disorder perturbations of integrable systems has a long history, at the other end, for strong disorder, a plethora of numerical phenomenology has been acquired over the last 5 years while the rigorous results are scarce with much room for fundamental improvement. One promising line of research is also shifting a paradigm from "what are the properties of a given system" to "how can one engineer a system with a given property".
Apart from deepening fundamental understanding of nonequilibrium statistical mechanics our goals shall also be in developing new mathematical and computational methods. Often such methods, which are developed for solving problems in theoretical physics, give new insights and concepts which bring even new developments into mathematics. As mathematical physics is not yet developed in Slovenia, we hope that our programme will be an important step in this direction.
Significance for science
The proposed research is a basic research in the field of mathematical (theoretical) physics. The questions we plan to address are very fundamental, e.g., stability to small imperfections, or deal with the simplest nonequilibrium setting, e.g., steady-state transport or dynamics (time-evolution) of local excitations. They are though of interest also in other areas of physics, for instance, in condensed-matter physics, statistical physics, or quantum information theory. With advancing quantum technologies and state-of-the-art experiments we are on the brink of having at our disposal quantum devices/simulations that surpass the best the classical technology can do. Understanding transport at the quantum level is a must if we want to master either very small devices or harness manifestations of quantum correlations on a mesoscopic scale or in observable properties. We thus believe that our theoretical and mathematical work should be highly relevant for the emerging quantum technologies.
Significance for the country
A goal of our new research programme, is to put mathematical physics - which is a traditional and well established field in world leading universities and fundamental research institutes - on the `research map' in Slovenia and to stimulate research cooperation between mathematics and theoretical physics. In Slovenia we have so far seen very little actual scientific collaboration between mathematics and theoretical physics. Principle investigator in this proposal T. Prosen, is, together with prof. Pavle Saksida, member of mathematics department, running a successful research seminar on mathematical physics at the Faculty of mathematics and physics since 2008. This has been the first step, which is expected to be embedded into the new research programme. We are also hosting frequent visits of mathematical physicists, mathematicians and theoretical physicists from abroad, and we continue to do so with even stronger intensity. Our program can thus be viewed as a 'cradle of mathematical physics' in Slovenia, which should in later stage also include research topics of mathematical physics other than those described above and support education and scientific development of mathematical physicists in Slovenia.
Most important scientific results
Interim report
Most important socioeconomically and culturally relevant results
Interim report
