EOAVENPVB2 Introduction to Solitons

Institute of physics in Opava
winter 2024
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Filip Blaschke, Ph.D. (lecturer)
RNDr. Filip Blaschke, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Filip Blaschke, Ph.D.
Institute of physics in Opava
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This lecture is an introduction to soliton physics in classical field theory with applications to Quantum Field Theory, particle physics, and condensed matter.
Learning outcomes
After finishing these lectures the student will:
- have basic knowledge about the 3 most common topological solitons, namely domain walls, magnetic vortices, and magnetic monopoles.
- be able to orient him/herself in integrable systems that are typified by the KdV equation.
- have a basic grasp of history and applications of solitons in various subfields of physics, most notably particle physics and condense matter physics.
Syllabus
  • The content of the lectures is made from several independent topics in which certain aspects of solitons are studied in detail. Major topics are:
  • • History of the discovery of solitons. Experiments of Scott. Fermi-Pasta-Ulam paradox.
  • • The KdV equation as wave equation for shallow cannals. Balance between dispersion and non-linear focusation. Solution of KdV equation for a single soliton and its properties. KdV solitons in Nature.
  • • Multi-soliton solutions of KdV equation via the Hirota method.
  • • Collisions of KdV solitons and the Inverse Scattering Method. Integrability. Lax pair. Hierarchy of conservation laws. Hierarchy of integrable systems.
  • • Solitons in scalar field theory and their scattering. The spectrum of fluctuations and the phenomenon of energy transfer between discrete modes. Sensitive dependence on initial velocity.
  • • Introduction to BPS theory. Completion of square and surface terms. Topological charge. Relation to supersymmetry.
  • • Sine-Gordon equation and its solutions. Balckund transform. Tachyons.
  • • Magnetic vortex. BPS solutions. Moduli-Matrix approach.
  • • `Dance' of magnetic vortices in Bose-Einstein condensate. Non-linear Schroedinger equation.
  • • Magnetic monopoles in classical electrodynamics. Dirac monopole. 't Hooft-Polyakov monopole. Magnetic monopoles in Standard Model. Montonen-Olive conjecture.
Literature
    recommended literature
  • Rajaraman, R. Solitons and Instantons, Elsevier Science Publishers, 1982
  • Shnir, Y. Magnetic Monopoles, Springer-Verlag Berlin Heidelberg, 2005
  • Manton, N., Sutcliffe, P. Topological solitons, Cambridge University Press, 2004
  • Lee, T. D., Pang, Y. Nontopological Solitons, Physics Reports, North-Holland, 1992
  • Nakahara, M. Geometry, Topology and Physics, IOP Publishing Ltd., 2003
Teaching methods
Lectures, presentations.
Assessment methods
A short (15 min.) presentation about the content of a scientific paper regarding solitons chosen by the student.
Language of instruction
English
Further Comments
The course is taught annually.
The course is taught: every week.
  • Enrolment Statistics (recent)
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