Application of Braid Groups in 2D Hall System Physics : Composite Fermion Structure.

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In the present treatise progress in topological approach to Hall system physics is reported, including recent achievements in graphene. The homotopy methods of braid groups turn out to be of particular convenience in order to grasp peculiarity of 2D charged systems upon magnetic field resulting in L...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Jacak, Janusz
Otros Autores: Gonczarek, Ryszard, Jacak, Lucjan
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore : World Scientific Publishing Company, 2012.
Temas:
Quantum Hall effect > Mathematical models.
Braid theory.
Effet Hall quantique > Modèles mathématiques.
Théorie des tresses.
SCIENCE > Physics > Quantum Theory.
Braid theory
Acceso en línea:Texto completo

MARC

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245 1 0 |a Application of Braid Groups in 2D Hall System Physics :  |b Composite Fermion Structure. 
260 |a Singapore :  |b World Scientific Publishing Company,  |c 2012. 
300 |a 1 online resource (160 pages) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
588 0 |a Print version record. 
505 0 |a Preface; Acknowledgments; Contents; 1. Introduction; 2. Elements of Hall system physics in 2D spaces; 2.1 Laughlin function; 2.2 Composite fermions; 2.2.1 Composite fermions in Jain's model; 2.2.2 Composite fermions in Read's model; 2.2.3 Local gauge transformations corresponding to Jain's flux tubes and Read's vortices in the structure of composite fermions; 3. Topological methods for the description of many particle systems at various manifolds; 3.1 Braid groups; 3.1.1 Full braid groups for R3, R2, sphere S2 and torus T; 3.1.2 Pure braid group. 
505 8 |a 3.2 Feynman integrals over trajectories and the relation with the one-dimensional unitary representations of the full braid group3.3 Bosons, fermions, anyons and composite particles; 3.3.1 Anyons on the plane, sphere and torus; 3.3.2 Quantum statistics and braid groups; 3.4 Multidimensional unitary irreducible representations of braid groups; 4. Cyclotron braids for multi-particle-charged 2D systems in a strong magnetic field; 4.1 Insufficient length of cyclotron radii in 2D systems in a strong magnetic field; 4.2 Definition of the cyclotron braid subgroup and its unitary representations. 
505 8 |a 4.3 Multi-loop trajectories-the response of the system to cyclotron trajectories that are too short4.4 Cyclotron structure of composite fermions; 4.5 The role of the Coulomb interaction; 4.6 Composite fermions in terms of cyclotron groups; 4.7 Hall metal in the description of cyclotron groups; 4.8 Comments on restrictions for the multi-loop structure of cyclotron braids; 4.8.1 Periodic character of wave packets' dynamics; 4.8.2 Quasi-classical character of quantization of the magnetic field flux; 4.9 Cyclotron groups in the case of graphene; 5. Recent progress in FQHE field. 
505 8 |a 5.1 The role of carrier mobility in triggering fractional quantum Hall effect in graphene5.2 Development of Hall-type experiment in conventional semiconductor materials; 5.3 Topological insulators-new state of condensed matter; 5.3.1 Chern topological insulators; 5.3.2 Spin-Hall topological insulators; 5.4 Topological states in optical lattices; 6. Summary; 7. Comments and supplements; 7.1 The wave function for a completely filled lowest Landau level; 7.2 Paired Pfaffian states; 7.2.1 Fermi sea instability toward the creation of Cooper pairs in the presence of particle attraction. 
505 8 |a 7.3 Basic definitions in group theory7.4 Homotopy groups; 7.4.1 Definition of homotopy; 7.4.2 Homotopic transformations; 7.4.3 Properties of homotopy; 7.4.4 Loop homotopy; 7.5 Configuration space; 7.5.1 First homotopy group of configuration space for many particle systems; 7.5.2 Covering space; 7.6 Braid groups for the chosen manifolds; 7.6.1 Braid group for a two-dimensional Euclidean space R2; 7.6.2 Braid group for a sphere S2; 7.6.3 Braid group for a torus T; 7.6.4 The braid group for the three-dimensional Euclidean space R3; 7.6.5 Braid group for a line R1 and a circle S1. 
500 |a 7.7 Exact sequences for braid groups. 
520 |a In the present treatise progress in topological approach to Hall system physics is reported, including recent achievements in graphene. The homotopy methods of braid groups turn out to be of particular convenience in order to grasp peculiarity of 2D charged systems upon magnetic field resulting in Laughlin correlations. The real progress in understanding of structure and role of composite fermions in Hall system is provided. The crucial significance of carrier mobility apart from interaction in creation of the fractional quantum Hall effect (FQHE) is described and supported by recent graphene. 
504 |a Includes bibliographical references (pages 135-144) and index. 
546 |a English. 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
590 |a eBooks on EBSCOhost  |b EBSCO eBook Subscription Academic Collection - Worldwide 
650 0 |a Quantum Hall effect  |x Mathematical models. 
650 0 |a Braid theory. 
650 6 |a Effet Hall quantique  |x Modèles mathématiques. 
650 6 |a Théorie des tresses. 
650 7 |a SCIENCE  |x Physics  |x Quantum Theory.  |2 bisacsh 
650 7 |a Braid theory  |2 fast 
700 1 |a Gonczarek, Ryszard. 
700 1 |a Jacak, Lucjan. 
758 |i has work:  |a Application of braid groups in 2D Hall system physics (Text)  |1 https://id.oclc.org/worldcat/entity/E39PCFF3rkDpJbmxjVHr6y6c4C  |4 https://id.oclc.org/worldcat/ontology/hasWork 
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856 4 0 |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=1143276  |z Texto completo 
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