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Introduction to Topological Defects and Solitons

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Produktnummer: 18a63be1d8cec54342855016749f562394
Autor: Selinger, Jonathan V.
Themengebiete: Defects in materials Disclination defects Dislocation defects Hedgehog defects Hopfions Skyrmions Solitons Topological defects textbook Topology in materials science Vortices
Veröffentlichungsdatum: 15.10.2024
EAN: 9783031701993
Sprache: Englisch
Seitenzahl: 213
Produktart: Kartoniert / Broschiert
Verlag: Springer International Publishing
Untertitel: In Liquid Crystals, Magnets, and Related Materials
Produktinformationen "Introduction to Topological Defects and Solitons"
This textbook introduces topological defects and solitons at a level suitable for advanced undergraduates and beginning graduate students in physics and materials science. It avoids the formal mathematics of topology, and instead concentrates on the physical properties of these topological structures.The first half of the book concentrates on fundamental principles of defects and solitons, and illustrates these principles with a single example—the xy model for 2D magnetic order. It begins by defining the concept of a winding number, and uses this concept to describe the topology of defects (vortices or disclinations) and solitons (domain walls), carefully identifying the similarities and differences between these two types of topological structures. It then goes on to discuss physical properties of defects and solitons, including free energy, dynamics, statistical mechanics, and coupling with curvature. It shows how these concepts emerge from a theory with variable magnitude of order, and hence how topology can be viewed as an approximation to physics.The second half goes on to explore a wider range of topological defects and solitons. First, it considers more complex types of order—2D nematic liquid crystals, 3D magnetic or liquid-crystal order, 2D or 3D crystalline solids—and shows how each type of order leads to specific topological structures. Next, it discusses defects and solitons that are characterized by 2D or 3D measuring surfaces, not just 1D loops, including hedgehogs, skyrmions, and hopfions. These structures are more complex, but they can still be understood using the same fundamental principles. A final chapter describes the formation of phases with regular arrays of defects or solitons.
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