Research programme is (co) funded by the Slovenian Research Agency.
UL Member: Faculty of Mathematics and Physics
Code: P1-0402
Programme: Mathematical physics
Period: 1. 1. 2015 - 31. 12. 2027
Range per year: 1,96 FTE category: C
Head: Tomaž Prosen
Research activity: Natural sciences and mathematics
Research organisations, researchers, citations for bibliographic records
Programme description:
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.
