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Application of braid groups in 2d hall system physics [[electronic resource] ] : composite fermion structure / / Janusz Jacak ... [et al.]
| Application of braid groups in 2d hall system physics [[electronic resource] ] : composite fermion structure / / Janusz Jacak ... [et al.] |
| Pubbl/distr/stampa | Singapore, : World Scientific, 2012 |
| Descrizione fisica | 1 online resource (160 p.) |
| Disciplina | 530.12 |
| Altri autori (Persone) | JacakJanusz |
| Soggetto topico |
Electrodynamics
Quantum theory Topology |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-299-28107-9
981-4412-03-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Acknowledgments; Preface; 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
3.2 Feynman integrals over trajectories and the relation with the one-dimensional unitary representations of the full braid group 3.3 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 4.3 Multi-loop trajectories-the response of the system to cyclotron trajectories that are too short 4.4 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 5.1 The role of carrier mobility in triggering fractional quantum Hall effect in graphene 5.2 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 7.3 Basic definitions in group theory 7.4 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 7.7 Exact sequences for braid groups |
| Record Nr. | UNINA-9910465395803321 |
| Singapore, : World Scientific, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Application of braid groups in 2d hall system physics [[electronic resource] ] : composite fermion structure / / Janusz Jacak ... [et al.]
| Application of braid groups in 2d hall system physics [[electronic resource] ] : composite fermion structure / / Janusz Jacak ... [et al.] |
| Pubbl/distr/stampa | Singapore, : World Scientific, 2012 |
| Descrizione fisica | 1 online resource (160 p.) |
| Disciplina | 530.12 |
| Altri autori (Persone) | JacakJanusz |
| Soggetto topico |
Electrodynamics
Quantum theory Topology |
| ISBN |
1-299-28107-9
981-4412-03-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Acknowledgments; Preface; 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
3.2 Feynman integrals over trajectories and the relation with the one-dimensional unitary representations of the full braid group 3.3 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 4.3 Multi-loop trajectories-the response of the system to cyclotron trajectories that are too short 4.4 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 5.1 The role of carrier mobility in triggering fractional quantum Hall effect in graphene 5.2 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 7.3 Basic definitions in group theory 7.4 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 7.7 Exact sequences for braid groups |
| Record Nr. | UNINA-9910792056903321 |
| Singapore, : World Scientific, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Application of braid groups in 2d hall system physics : composite fermion structure / / Janusz Jacak ... [et al.]
| Application of braid groups in 2d hall system physics : composite fermion structure / / Janusz Jacak ... [et al.] |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Singapore, : World Scientific, 2012 |
| Descrizione fisica | 1 online resource (160 p.) |
| Disciplina | 530.12 |
| Altri autori (Persone) | JacakJanusz |
| Soggetto topico |
Electrodynamics
Quantum theory Topology |
| ISBN |
1-299-28107-9
981-4412-03-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Acknowledgments; Preface; 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
3.2 Feynman integrals over trajectories and the relation with the one-dimensional unitary representations of the full braid group 3.3 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 4.3 Multi-loop trajectories-the response of the system to cyclotron trajectories that are too short 4.4 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 5.1 The role of carrier mobility in triggering fractional quantum Hall effect in graphene 5.2 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 7.3 Basic definitions in group theory 7.4 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 7.7 Exact sequences for braid groups |
| Record Nr. | UNINA-9910816078403321 |
| Singapore, : World Scientific, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||