LEADER 09352nam 2200565 450 001 9910616384203321 005 20230727165155.0 010 $a9783031095283$b(electronic bk.) 010 $z9783031095276 035 $a(MiAaPQ)EBC7102390 035 $a(Au-PeEL)EBL7102390 035 $a(CKB)24950538500041 035 $a(PPN)264960742 035 $a(EXLCZ)9924950538500041 100 $a20230226d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe theory of the Jahn-Teller effect $ewhen a boson meets a fermion /$fArnout Ceulemans 210 1$aCham, Switzerland :$cSpringer,$d[2022] 210 4$d©2022 215 $a1 online resource (429 pages) 311 08$aPrint version: Ceulemans, Arnout The Theory of the Jahn-Teller Effect Cham : Springer International Publishing AG,c2022 9783031095276 320 $aIncludes bibliographical references and index. 327 $aIntro -- Preface -- Contents -- Part I Bosons and Fermions -- 1 The Impossible Theorem -- Contents -- 1.1 The Jahn-Teller Theorem -- 1.2 Charge Density Analysis -- 1.2.1 Occupation of dz2 -- 1.2.2 Occupation of dx2-y2 -- 1.2.3 Sum and Difference Orbitals -- 1.2.4 Orthogonal and Unitary Combinations -- 1.3 Outlook -- References -- 2 Bosons and Fermions -- Contents -- 2.1 Bosons -- 2.1.1 The Schrödinger Formalism -- 2.1.2 The Dirac Formalism -- 2.1.3 The Bargmann Mapping -- 2.2 Fermions -- 2.2.1 Fermion Operators -- 2.2.2 One-Electron Interactions -- 2.2.3 Quasi-Spin -- References -- 3 Boson-Fermion Interactions -- Contents -- 3.1 The Jahn-Teller Effect in a Triangular Molecule: A Toy Model -- 3.1.1 The Hückel Hamiltonian -- 3.1.2 Fermions: Trigonal Molecular Orbitals -- 3.1.3 Bosons: Vibrational Modes -- 3.1.4 Coupling Coefficients -- 3.2 Degeneracies and Time Reversal -- 3.2.1 Time Reversal -- 3.2.2 Irreducible Representations of the First Kind and Orthogonal Lie Groups -- 3.2.3 Irreducible Representations of the Second Kind and Symplectic Lie Groups -- 3.2.4 Irreducible Representations of the Third Kind -- 3.3 The Jahn-Teller Hamiltonian -- 3.4 Selection Rules -- 3.4.1 Space Symmetry -- 3.4.2 Time Reversal Symmetry -- 3.4.3 Hole-Particle Exchange Symmetry -- 3.5 Proof of the Jahn-Teller Theorem -- 3.5.1 History -- 3.5.2 Where Do Degeneracies Come From? -- 3.5.2.1 Cosets and the Positional Representation -- 3.5.2.2 Doubly Transitive Orbits -- 3.5.3 Degenerate Representations and Jahn-Teller Modes -- 3.5.4 Jahn-Teller Activity in Simplexes -- References -- Part II Dynamic Symmetries -- 4 The Rabi Hamiltonian -- Contents -- 4.1 The Adiabatic Potential -- 4.2 The Quantum Model -- 4.3 Bargmann Mapping of the Wave Equations -- 4.4 Eigenvalues -- 4.4.1 Classification of the Roots -- 4.4.2 Recurrence Relations and Transcendental Function. 327 $a4.4.3 The Rabi Spectrum -- 4.5 The Quantization of the Rabi Hamiltonian -- 4.6 Analyticity -- 4.7 Inversion Tunneling in Ammonia -- References -- 5 The E ×e Orbital Doublet -- Contents -- 5.1 The Quantum Model -- 5.2 Dynamic Symmetries -- 5.2.1 Boson Symmetry -- 5.2.2 Fermion Symmetry -- 5.2.3 Coupled Symmetries -- 5.3 The Canonical Form of the Wave Equation -- 5.4 Recurrence Relationships -- 5.5 Results -- 5.6 Discussion -- 5.7 Application: Na3 and the (E+A)×e Hamiltonian -- References -- 6 The Spin Quartet ?8 ×(e+t2) System and the Symplectic Group Sp(4) -- Contents -- 6.1 Historical Note: Judd and Reik -- 6.2 The Hamiltonian -- 6.2.1 The Static Case -- 6.2.2 The Dynamic Hamiltonian -- 6.3 Sp(4) Fermion Symmetry -- 6.4 SO(5) Boson Symmetry -- 6.5 The ?8 ×(e+t2) Dynamic Equations -- 6.6 The ?8 ×t2 Subsystem -- 6.6.1 SO(3) Invariance -- 6.6.2 Dynamic Equations -- 6.7 Application -- 6.7.1 ReF6 -- 6.7.2 IrF6 -- References -- 7 Ansatz for the Jahn-Teller Triplet Instability -- Contents -- 7.1 SO(5) Symmetry and the Five-Dimensional Harmonic Oscillator -- 7.1.1 SU(5) ? SO(5) Symmetry Breaking -- 7.1.2 SO(5) ? SO(3) Symmetry Breaking -- 7.2 The Hamiltonian -- 7.3 The Vibrating Sphere -- 7.4 Boson Functions -- 7.4.1 S States -- 7.4.2 D States -- 7.4.3 F States -- 7.5 The Ansatz -- 7.6 The Jahn-Teller Equations -- 7.7 Solution -- 7.8 Ansatz for Vibronic D States -- 7.9 Application -- 7.10 Conclusion -- References -- 8 The Icosahedral Quartet and SO(9) ? SO(4) Symmetry Breaking -- Contents -- 8.1 Introduction -- 8.2 Preamble: Hyperspherical Symmetry -- 8.3 The Hamiltonian -- 8.4 The Vibrations of the Four-Dimensional Hypersphere -- 8.5 SO(9) ? SO(4) Symmetry Breaking -- 8.5.1 (0,0) Modes -- 8.5.2 (1,1) Boson Modes -- 8.5.3 Modes with Seniority ?> -- 4 -- 8.6 The Ansatz: Vibronic (12,12) Levels -- 8.7 Icosahedral Symmetry Lowering. 327 $a8.8 Application: C20 and C80 Fullerenes -- 8.8.1 C20 -- 8.8.2 C80 -- References -- 9 SO(14) ? SO(5) Symmetry Breaking and the Jahn-Teller Quintet Instability -- Contents -- 9.1 Dynamic Symmetries -- 9.2 Descent to Spherical Symmetry -- 9.2.1 Branching Rules for SO(5) SO(3) -- 9.2.2 The L=2 Case -- 9.2.3 The L=4 Case -- 9.3 Descent to Permutational Symmetry -- 9.3.1 The Icosahedral Hamiltonian -- 9.3.2 The Hexateron -- 9.4 Correlation Between the Spherical and the Permutational Scheme -- 9.5 Application: The Ground State of C60+ Cation -- References -- 10 Jahn's and Teller's Last Case: The Spinor Sextet -- Contents -- 10.1 Group Theory of the Sextet Spinor -- 10.1.1 The Unitary Symplectic Group USp(6) -- 10.1.2 The SO(14) Group of the Bosons -- 10.2 The ?9 ×(g+2h) Problem -- 10.2.1 The Hamiltonian -- 10.2.2 Diagonalization -- 10.2.3 The Equal Coupling Case -- 10.3 Chemical Applications -- 10.4 Overview -- 10.4.1 Orbital Representations: SO(N) ? SO(n) -- 10.4.2 Spinor Representations: SO(N) ? USp(2n) -- References -- Part III Topography -- 11 Conical Intersections and Quantum Fields -- Contents -- 11.1 The Berry Phase -- 11.1.1 The Quantal Phase Factor Accompanying Adiabatic Changes -- 11.1.1.1 Single-Valued Basis Functions -- 11.1.1.2 Real Basis Sets -- 11.1.2 Holonomy -- 11.2 The E×e Jahn-Teller Case -- 11.2.1 Berry Phase for the E×e Case -- 11.2.2 The Dirac Monopole Analogy -- 11.2.3 Berry Phase and Angular Momentum -- 11.3 Quadruple Spin Degeneracy and the Instanton -- 11.3.1 The ?8 ×t2g Hamiltonian -- 11.3.2 The ?8 ×(eg+t2g) Hamiltonian -- References -- 12 Topography and Chemical Reactivity -- Contents -- 12.1 Tools -- 12.1.1 The Epikernel Principle -- 12.1.2 The Isostationary Function -- 12.1.3 Proof of the Epikernel Principle -- 12.1.3.1 Only One ? Irrep -- 12.1.3.2 More than One ? Irrep -- 12.1.3.3 Illustration: The ?×(?1+?2) Problem. 327 $a12.2 Orbital Doublets -- 12.2.1 The E×(b1+b2) System -- 12.2.2 The E×e System -- 12.2.3 The Pentagonal E1×e2 Problem -- 12.3 The Cubic T×(e+t2) Problem -- 12.3.1 Second-Order Warping Terms -- 12.3.2 Chemical Reactivity: The Isomerization of Fe(CO)4 -- 12.4 The Icosahedral T ×h System -- 12.5 The Icosahedral G×g+h Quartet System -- 12.5.1 The Isostationary Function -- 12.5.2 Tetrahedral Minima -- 12.5.3 Trigonal Minima -- 12.6 The Icosahedral H×(g+2h) Quintet System -- 12.6.1 The Isostationary Function -- 12.6.2 Pentagonal Minima -- 12.6.3 Trigonal Minima -- 12.7 The Icosahedral ?9 ×(g+2h) Sextet System -- 12.7.1 The G-Type Subspace -- 12.7.2 The H Subspace -- 12.7.2.1 The FH2 Hamiltonian at ?=0? -- 12.7.2.2 Trough Solution: T1 ×?7: ??100.893? -- 12.7.2.3 Trough Solution: T2 ×?6: ??220.8934 -- References -- Epilogue -- A The Displaced Oscillator -- Contents -- A.1 Hamiltonian -- A.2 The Displacement Operator -- A.3 Eigenfunction of the Annihilation Operator -- A.4 Matrix Representation of the Displaced Oscillator -- References -- B Derivation of the Coupling Coefficients -- Contents -- B.1 Clebsch-Gordan Coupling Coefficients -- B.2 How to Calculate Coupling Coefficients -- B.3 Icosahedral States -- References -- C SU(n), SO(n), Sp(2n) Lie Algebras -- Contents -- C.1 The Special Unitary Group SU(n) -- C.2 The Special Orthogonal Group SO(n) -- C.3 The Symplectic Group Sp(2n) -- References -- D The Birkhoff Transformation -- Contents -- D.1 The Birkhoff Theorem -- D.2 Transformation of the Rabi Equation to the Standard Birkhoff Form -- D.3 Recursion Formulas for the Rabi Case -- D.4 Summary -- References -- E Dirac's Monopole -- Contents -- E.1 The Field of a Monopole -- E.2 The Vector Potential -- References -- F Yang's Monopole -- Contents -- F.1 Introduction -- F.2 The Tensor Potential A -- F.3 The Field Tensor F -- References. 327 $aG Topological Graph Theory -- Contents -- G.1 Graphs -- G.2 Rings -- G.3 Faces -- References -- Compound Index -- Subject Index. 606 $aInteracting boson-fermion models 606 $aJahn-Teller effect 606 $aEfecte Jahn-Teller$2thub 606 $aBosons$2thub 606 $aFermions$2thub 608 $aLlibres electrònics$2thub 615 0$aInteracting boson-fermion models. 615 0$aJahn-Teller effect. 615 7$aEfecte Jahn-Teller 615 7$aBosons 615 7$aFermions 676 $a530.143 700 $aCeulemans$b Arnout$01260221 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910616384203321 996 $aThe Theory of the Jahn-Teller Effect$92920193 997 $aUNINA LEADER 03443nam 2200565 450 001 9910811303003321 005 20240116064057.0 010 $a1-68417-627-1 024 7 $a10.1163/9781684176274 035 $a(CKB)4900000001453270 035 $z(OCoLC)1141443117 035 $a(nllekb)BRILL9781684176274 035 $a(MiAaPQ)EBC30672009 035 $a(Au-PeEL)EBL30672009 035 $a(OCoLC)1302738863 035 $a(MdBmJHUP)musev2_113535 035 $a(EXLCZ)994900000001453270 100 $a20240116d2020 uy 0 101 0 $aeng 135 $aurun####uuuua 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $2rdacarrier 200 12$aA Third Way $eThe Origins of China's Current Economic Development Strategy /$fLawrence C. Reardon 205 $aFirst edition. 210 1$aCambridge, Massachusetts :$cHarvard University Asia Center,$d[2020] 210 4$d©2020 215 $a1 online resource 225 1 $aHarvard East Asian Monographs ;$vVolume 438 311 $a0-674-24788-4 320 $aIncludes bibliographical references and index. 327 $aIntroduction: Elite learning and China's third way -- Empowering the coastal provinces, 1978-80 -- Initiating the special economic zones, 1980-81 -- Review and adjustment of the experiment, 1981-83 -- Coastal expansion, 1983-88 -- Initiating China's third way --Conclusion: Spillover and the Stalinist paradigm. 330 $a"From 1949 to 1978, communist elites held clashing visions of China's economic development. Mao Zedong advocated the "first way" of semi-autarchy characteristic of revolutionary Stalinism (1929-34), while Zhou Enlai adapted bureaucratic Stalinism (1934-53) to promote the "second way" of import substitution industrialization. A Third Way tells the story of Deng Xiaoping's experimentation with export-led development inspired by Lenin's New Economic Policy and the economic reforms of Eastern Europe and Asia. Having uncovered an extraordinary collection of internal party and government documents, Lawrence Reardon meticulously traces the evolution of the coastal development strategy, starting with special economic zones in 1979 and evolving into the fourteen open coastal cities, the Hainan SEZ, and eventual accession to the global trade regime in 2001. Reardon details how Deng and Zhao Ziyang tackled large-scale smuggling operations, compromised with Chen Yun's conservative views, and overcame Deng Liqun's ideological opposition. Although Zhao Ziyang was airbrushed out of official Chinese history after June 4, 1989, Reardon argues that Zhao was the true architect of China's opening strategy. A Third Way provides important new insights about the crucial period of the 1980s and how it paved the way for China's transformation into a global economic superpower"--Provided by publisher. 410 0$aHarvard East Asian monographs ;$vVolume 438. 606 $aCommunism$zChina$xHistory$y20th century 606 $aMixed economy 606 $aMixed economy$zChina$xHistory$y20th century 607 $aChina$xEconomic policy$y1949-1976 615 0$aCommunism$xHistory 615 0$aMixed economy. 615 0$aMixed economy$xHistory 676 $a335.4345 700 $aReardon$b Lawrence C.$0944129 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910811303003321 996 $aA Third Way$94086353 997 $aUNINA