Exploring dissipative systems with non-Hermitian modulations

Author: Salim Benadouda i Ivars

Title: Exploring dissipative systems with non-Hermitian modulations

Supervisors: Ramon Herrero Simon (director) i Kestutis Staliunas (co-director).

Presentation date: 14th February 2025

Link to text: https://www.tesisenred.net/handle/10803/693894

Abstract: The aim of this thesis is to explore the effect of non-Hermitian potentials in different nonlinear systems. Specifically, in the different sections of this work we focus on the stabilisation of various states. We consider mainly two systems due to their universality: the Gizburg Landau and the Lugiato Lefever equations. Both models correspond to generalisations of the nonlinear Schrödinger equation. The Ginzburg-Landau equation represents the dissipative extension of physical systems with active media. It has been extensively studied and praised as a foundational model for phenomena such as turbulence, lasers or Bose Einstein condensates. In contrast, the Lugiato-Lefever equation addresses dissipative systems with lossy media, where energy is injected. Recently, this model has gained renewed attention due to its accurate representation of fields in micro-resonators and the rapid advancements in mastering their fabrication. Through analytical and numerical studies we investigate how introducing non-Hermitian potentials leads to the stabilisation of different coherent structures. For laser-like models that exhibit strong and persistent turbulence regimes, this approach results in an effective stabilisation and control of the system. In turn, for micro-resonators, the stabilisation of periodic structures uncovers a novel and hybrid formation mechanism for solitons.