PROLHAC Sylvain

Address: Laboratoire de Physique Théorique,
Université de Toulouse, 118 Route de Narbonne,
31062 Toulouse Cedex 4, France

I have been working recently on a one-dimensional non-equilibrium universality class known as KPZ, which describes the fluctuations of some growing interfaces as well as classical and quantum fluids.

I am especially interested in finite volume effects, corresponding to a regime where the correlation length of the fluctuations is of the same order of magnitude as the size of the system. The temporal evolution of the system then describes all the relaxation process of the fluctuations between some initial state and the stationary state.

On the technical side, current fluctuations for the totally asymmetric simple exclusion process (TASEP) involve contour integrals on a compact Riemann surface, which depends on boundary conditions, and whose genus tends to infinity in the scaling limit to KPZ fluctuations in finite volume.

 

ASEP and the corresponding interface growth model

Riemann surface TASEP (2 particles on 5 sites) : sphere

Riemann surface TASEP (3 particles on 7 sites) : torus

Recent oral presentations

• Habilitation thesis defense, 15 January 2024

Selected papers (full list on arXiv):

 Review paper, based on my habilitation thesis :

• S.Prolhac, KPZ fluctuations in finite volume, arXiv:2401.15016

 Exact formulas for KPZ fluctuations with periodic boundaries

• S. Prolhac, Finite-time fluctuations for the totally asymmetric exclusion process, Phys. Rev. Lett. 116 (2016) 090601 (arXiv:1511.04064)

 Probability as a contour integral on a Riemann surface

• S. Prolhac, Riemann surfaces for KPZ with periodic boundaries, SciPost Phys. 8, 008 (2020) (arXiv:1908.08907)
• S. Prolhac, Riemann surface for TASEP with periodic boundaries, J. Phys. A: Math. Theor. 53 445003 (2020) (arXiv:2006.15096)
• S. Prolhac, Riemann surfaces for integer counting processes, J. Stat. Mech. (2022) 113201 (arXiv:2206.01698)
• S. Prolhac, Probability of a single current, arXiv:2308.11693

 Spectrum

• S. Prolhac, Perturbative solution for the spectral gap of the weakly asymmetric exclusion process, J. Phys. A: Math. Theor. (2017) 50:315001 (arXiv:1703.04596)
• U. Godreau and S. Prolhac, Spectral gaps of open TASEP in the maximal current phase, J. Phys. A: Math. Theor. (2020) 53 385006 (arXiv:2005.04461)

 Stationary limit: non-intersecting Brownian bridges

• S. Prolhac and K. Mallick, Brownian bridges for late time asymptotics of KPZ fluctuations in finite volume, J. Stat. Phys. 173 (2018) 322-361 (arXiv:1805.03187)