LEADER 05341nam 2200661Ia 450 001 9910816078403321 005 20240313172850.0 010 $a1-299-28107-9 010 $a981-4412-03-1 035 $a(CKB)2560000000099517 035 $a(EBL)1143276 035 $a(OCoLC)830162007 035 $a(SSID)ssj0000912936 035 $a(PQKBManifestationID)11523318 035 $a(PQKBTitleCode)TC0000912936 035 $a(PQKBWorkID)11013286 035 $a(PQKB)11142196 035 $a(MiAaPQ)EBC1143276 035 $a(WSP)00002903 035 $a(Au-PeEL)EBL1143276 035 $a(CaPaEBR)ebr10674384 035 $a(CaONFJC)MIL459357 035 $a(EXLCZ)992560000000099517 100 $a20120520d2012 uy 0 101 0 $aeng 135 $aurcuu|||uu||| 181 $ctxt 182 $cc 183 $acr 200 00$aApplication of braid groups in 2d hall system physics $ecomposite fermion structure /$fJanusz Jacak ... [et al.] 205 $a1st ed. 210 $aSingapore $cWorld Scientific$d2012 215 $a1 online resource (160 p.) 300 $aDescription based upon print version of record. 311 $a981-4412-02-3 320 $aIncludes bibliographical reference (p. 135-144) and index. 327 $aAcknowledgments; 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 327 $a3.2 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 327 $a4.3 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 327 $a5.1 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 327 $a7.3 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 327 $a7.7 Exact sequences for braid groups 330 $aIn 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 606 $aElectrodynamics 606 $aQuantum theory 606 $aTopology 615 0$aElectrodynamics. 615 0$aQuantum theory. 615 0$aTopology. 676 $a530.12 701 $aJacak$b Janusz$0732443 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910816078403321 996 $aApplication of braid groups in 2D Hall system physics$91443043 997 $aUNINA