|09:30 to 11:00||Tomaz Prosen (University of Ljubljana, Slovenia)||Solvable models of diffusion and many-body chaos (Lecture 2)|
|11:30 to 13:00||Benjamin Doyon (King's College London, UK)||
Generalised hydrodynamics (Lecture 1)
Hydrodynamics is a powerful theory for describing the emergent dynamics, away from equilibrium, at large scales in space and time. In recent years, the theory adapting hydrodynamics to integrability, called ``generalised hydrodynamics” (GHD), has been developed. It turns out to be extremely general, applicable to quantum and classical chains, field theories and gases. These lectures will cover the fundamental concepts of this theory. Starting from an overview of hydrodynamics, I will describe the most important aspects of integrability, from which I will derive the basic GHD equations. I will emphasise the universality of GHD and the physical interpretation of its various ingredients, and if time allows, explain some of its applications and more advanced concepts. Only very basic knowledge of hydrodynamics and integrability is assumed, and I will keep everything as non-technical as possible.
|14:30 to 15:10||Tomaz Prosen (University of Ljubljana, Slovenia)||The Rule 54: Exactly solvable deterministic interacting model of transport|
|15:10 to 15:50||Manas Kulkarni (ICTS, India)||
Kardar Parisi Zhang (KPZ) scaling in non-integrable and integrable classical models
We will discuss spatio-temporal correlations in classical non-integrable and integrable models. We start with earlier works on discrete Nonlinear Schrodinger Equation [1,2] and then present results on equilibrium spatio-temporal correlations in classical non-integrable and integrable spin chains. For the non-integrable case, we consider the classical XXZ model (Lattice Landau Lifshitz model) and show regimes where we find KPZ scaling . We explain it using the framework of nonlinear fluctuating hydrodynamics (NFH). To our surprise, we find that a classical integrable spin chain (Integrable Lattice Landau Lifshitz model) also has regimes in which it displays KPZ behaviour . Our findings are along the lines of what was recently found in quantum integrable spin chains thereby providing strong evidence for a classical-quantum correspondence.
 Manas Kulkarni, Austen Lamacraft, Phys. Rev. A 88, 021603, Rapid Communications 
|16:20 to 17:00||Anupam Kundu (ICTS, India)||
Equilibrium density of confined particles with repulsive interaction
Systems of interacting particles confined in external potentials are ubiquitous in nature. Particularly, pairwise repulsive interactions with power-law divergences have taken a special place in physics and mathematics. I will discuss a system of N classical particles interacting via pairwise repulsive interaction potential. They are also confined by an external potential which tries to pull them to its minimum. On the other hand the interaction and the entropy try to spread them apart. As a result they settle down over some region with an inhomogeneous density. By deriving a large-N macroscopic description in terms of free energy functional (action) and then minimising it, it is possible to find various interesting distributions of the particles. I will show how the range of interaction as well as the form of the external potential affect this density.