Research project is (co) funded by the Slovenian Research Agency.

**UL Member:** Faculty of Mathematics and Physics**Code:** N1-0055**Project:** Thermalization in non-equilibrium quantum systems**Period:** 1.6.2016 - 31.5.2019 **Range per year:** 0,68 FTE, category A**Head:** Tomaž Prosen **Research activity:** Natural sciences and mathematics**Research Organisations:** link on SICRIS**Researchers:** link on SICRIS**Citations for bibliographic records:** link on SICRIS

**Project description:**

Recent technological developments - especially in the field of trapped ultra cold atoms - have made possible the direct experimental study of the dynamics of (almost) closed interacting quantum systems out of equilibrium. This allows experimental study and analysis of fundamental problems of quantum statistical mechanics, such as thermalisation (ie. evolution towards equilibrium), its conditions and mechanism, the generation of entropy, the effects of integrability and its breaking, the structure of current carrying steady states, and detailed analysis of the behaviour of driven quantum systems.

The proposed research aims at a theoretical exploration of these problems, and the development of the necessary new theoretical methods. This is based on the complementary expertise of the Slovenian and Hungarian partners, within an intensive cooperation, involving PhD and MSc students in the work on both sides.

The methods we plan to develop (semi-semiclassical theory, non-Abelian time evolving block decimation, Liouville-space DMRG) are to be compared to each other and analytical methods. We shall apply them to interacting systems and models directly realizable with trapped ultracold atoms.

The fundamental questions we aim to explore are:

- Do various systems thermalize and under what conditions? How the thermal state is approached, and what determines the characteristic relaxation times-scales?
- What is the role of various types of conserved quantities (local, quasi-local, non-local etc.) in the process?
- How do non-thermal steady states, such as the ones supporting nonzero currents, form? What is the dynamical structure of such states, and how are they related with the physics of systems driven by external forces?
- What is the the precise role of integrability and its breaking in the thermalization process?
- New dynamical phenomena observable during thermalization (e.g., prethermalization or a cascade of intermediate quasistationary states).

Our collaboration is aimed at developing new methods to answer the above questions, and to apply them to experimentally relaized strongly correlated systems, such as e.g.

- strongly interacting Bose gases,
- quantum spin chains, and
- quantum field theories providing a largely universal long-distance description of condensed matter systems (carbon nanotubes, organic macromolecules, superconducting quantum wires).

Our final goal is to describe and understand experimentally observable phenomena.