Mathematical Aspects of Quantum Integrable Models in and out of Equilibrium

Quantum Integrability is a rich and highly cross-disciplinary subject, with fascinating mathematical structures and a wide spectrum of physical applications. It is the key tool for understanding critical properties of numerous quantum systems at and out of equilibrium, such as spin chains or the delta-function Bose gas (also known as the quantum non-linear Schrödinger equation). Long-standing problems such as the scaling limit of the Ising model in a magnetic field have been solved thanks to recent developments of integrable techniques.

These developments in theoretical physics have been paralleled by advances in several areas of pure and applied mathematics, enhancing interactions among researchers working on combinatorics, probability theory, infinite dimensional Lie algebras, knots and braids, soliton systems, random matrices, non-linear differential equations and computational science.

A new arena for quantum integrable systems has recently arisen as a result of the ability to realize for the first time, stable and controllable isolated quantum systems (by means of cold atom experimental set-ups). This has led to an immense growth of this research area and has given access to a largely unexplored territory of out-equilibrium quantum dynamics.

These exciting advances call for the development of new mathematical techniques to meet the challenge of describing out-of-equilibrium phenomena in strongly interacting lowdimensional quantum systems.

In gathering together a core group of outstanding scientists, we aim to make substantial progress on a series of key open problems. Topics will include

Quantum Quenches Boundary Conformal Field Theory Driven Systems Local and non-local conserved charges Boltzmann equation and transport phenomena Entanglement measures Linear and non-linear response Non-linear hydrodynamics Thermalization and Equilibration in Quantum Systems Generalized Gibbs Ensemble Dynamics of quantum integrable systems Open quantum systems Techniques in atomics condensate

Activities

In the first week of the programme there will be a conference, that will gather together leading physicists and mathematicians in the area of Quantum Integrability. In each of the following weeks there will be two introductory 60 minute lectures by world-leading experts. The topics of the lectures will be chosen to mesh with Focus Week Activities planned to involve the participants on key themes of the programme. During the Focus Weeks there will also be a certain number of round table discussions that will help in exploiting new scientific directions and shaping the future research on this emerging field.