2020/09/30 by Mariya Lizunova, Jasper van Wezel · 6 citations
Physics and Astronomy · #Complex system #Cosmology #Living matter #Nonlinear Photonic Systems #Orbital Angular Momentum in Optics #Phenomenology (philosophy) #Quantum chaos and dynamical systems #Scattering #Topological defect #cond-mat.other #nlin.PS
paper · pdf · doi:10.21468/scipostphyslectnotes.23
published in SciPost Physics Lecture Notes (SciPost.org) · 27 pages, submitted to SciPost Physics Lecture Notes; small updates
openalex created_date 2020/09/08 · arxiv created 2020/12/10 · arxiv updated 2021/02/03 · openalex publication_date 2021/02/03 · openalex updated_date 2026/08/05
As a low-energy effective model emerging in disparate fields throughout all of physics, the ubiquitous φ4 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>φ</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:math> -theory is one of the central models of modern theoretical physics. Its topological defects, or kinks, describe stable, particle-like excitations that play a central role in processes ranging from cosmology to particle physics and condensed matter theory. In these lecture notes, we introduce the description of kinks in φ4 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>φ</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:math> -theory and the various physical processes that govern their dynamics. The notes are aimed at advanced undergraduate students, and emphasis is placed on stimulating qualitative insight into the rich phenomenology encountered in kink dynamics. The appendices contain more detailed derivations, and allow enquiring students to also obtain a quantitative understanding. Topics covered include the topological classification of stable solutions, kink collisions, the formation of bions, resonant scattering of kinks, and kink-impurity interactions.