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29 November 2023 Wed 2 pm

The cubic complex Ginzburg-Landau equation is one of the most-studied nonlinear equations in the physics community. It describes a vast variety of phenomena from nonlinear waves to second-order phase transitions, from superconductivity, superfluidity, and Bose-Einstein condensation to liquid crystals and strings in field theory. In this two lectures, I’ll give an overview of various phenomena described by the complex Ginzburg-Landau equation in one, two, and three dimensions from the point of view of condensed-matter physicists. Their aim is to study the relevant solutions in order to gain insight into nonequilibrium phenomena in spatially extended systems.

* * *  Lecture 1  * * *

Introduction

Simple Model – Rich Phenomenology

Plane Waves and Their Stability

Absolute vs Convective Instability

Topological Defects, Sinks and Sources

Core Instability of Defects

* * *  Lecture 2  * * *

1D Chaos and Intermittency

2D Spirals Waves

Stability of Spiral Waves

Interaction of Spiral Waves

Vortex Glass and Vortex Liquid

3D vortex lines and their dynamics

Open questions