Topological structures for KPZ universality with boundaries

Stage M2

Lieu d'accueil :
Laboratoire de Physique Théorique, Toulouse

Contact :
Sylvain Prolhac, Toulouse

Court résumé :

KPZ universality describes the dynamics of large scale fluctuations in a variety of settings, such as growing interfaces or one-dimensional fluids. It has become in the past few years a prominent topic at the interface between non-equilibrium statistical physics (theory and experiments) and mathematics (probability, combinatorics, random matrices, harmonic analysis). At the KPZ fixed point, the fundamental object of interest is a very singular random field depending on space and time. Despite several exact results and nice experiments in the past twenty years, the nature of the field theory behind the KPZ fixed point remains largely mysterious.

A powerful approach to the KPZ fixed point is through deceptively simple microscopic models, such as the totally asymmetric simple exclusion process (TASEP), which is exactly solvable using Bethe ansatz integrability. During the internship, the student will familiarize herself/himself with Bethe ansatz in the context of KPZ universality, and will attempt to obtain new asymptotic results about the spectrum of TASEP with open boundaries.

Building on recent progress about quasi-particle excitations in finite volume, the aim of the thesis will be to understand the effects of boundary conditions connecting a system from KPZ universality to an external environment. Of special interest will be the topology of complex analytic structures describing the underlying phase space, which are expected to differ significantly from that of KPZ with periodic boundaries. The techniques used will combine large scale asymptotics of TASEP Bethe eigenstates, as well as a recent mapping to extreme value statistics of Brownian motions, dealing directly with the KPZ fixed point in the continuum.

More information can be found on my webpage