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

**UL Member:** Faculty of Mathematics and Physics

**Code:** N1-0109

**Project:** Quenches, Transport and Entanglement in one-dimensional quantum systems out-of-equilibrium

**Period:** 1. 1. 2019 - 31. 12. 2020

**Range per year:** 1 FTE, **category:** E

**Head:** Spyridon Sotiriadis

**Research activity**: Natural sciences and mathematics

**Citations for bibliographic records**

**Project description:**

One of the fundamental questions of theoretical physics is how the laws of quantum dynamics can be reconciled with the emergence of statistical mechanics. The aim of the proposed research is to tackle some highly topical or long-standing problems related to this question, by means of mathematically rigorous yet physically intuitive methods.

Specifically, we will focus on three classes of physical problems:

i) Quantum quenches: We will derive analytical and numerical predictions for the time evolution of physical observables after an abrupt parameter change in experimentally relevant models of one-dimensional cold-atom systems. We will compare our results in collaboration with experimentalists who have recently achieved the first observation of a Generalised Gibbs Ensemble, describing the long-time steady state after such a quench.

ii) Quantum transport: We will analytically derive from first principles the Non-Equilibrium Steady State that emerges after a quench in an integrable system, when starting from an inhomogeneous initial state. We will verify the validity of a Generalised Hydrodynamics approach that has been recently conjectured and describes successfully the steady state.

iii) Entanglement Entropy: We will develop a new analytical method for the study of entanglement entropy in ground or equilibrium states of interacting models and apply it for the study of its scaling, as well as its growth and saturation after a quench.

We aim to unveil certain aspects of the mechanism of quantum equilibration, developing analytical tools of broad applicability. We will try to bring closer the quantum many-body physics, quantum information and field theoretical approaches to out-of-equilibrium physics, by communicating our findings to these different communities.