IBS Center for Theoretical Physics of Complex Systems (PCS), Administrative Office (B349), Theory Wing, 3rd floor

                                      Expo-ro 55, Yuseong-gu, Daejeon, South Korea, 34126 Tel: +82-42-878-8633                     

Igor Aronson

Pennsylvania State University, USA

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  * * *


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

  1. introduction into the complex ginzburg-landau equation. part 2