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The theory of the Jahn-Teller effect : when a boson meets a fermion / / Arnout Ceulemans
The theory of the Jahn-Teller effect : when a boson meets a fermion / / Arnout Ceulemans
Autore Ceulemans Arnout
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (429 pages)
Disciplina 530.143
Soggetto topico Interacting boson-fermion models
Jahn-Teller effect
Efecte Jahn-Teller
Bosons
Fermions
Soggetto genere / forma Llibres electrònics
ISBN 9783031095283
9783031095276
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- 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.
4.4.3 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 Γ8 ×(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 Γ8 ×(e+t2) Dynamic Equations -- 6.6 The Γ8 ×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 ν> -- 4 -- 8.6 The Ansatz: Vibronic (12,12) Levels -- 8.7 Icosahedral Symmetry Lowering.
8.8 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 Γ9 ×(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 Γ8 ×t2g Hamiltonian -- 11.3.2 The Γ8 ×(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 Λ Irrep -- 12.1.3.2 More than One Λ Irrep -- 12.1.3.3 Illustration: The Γ×(Λ1+Λ2) Problem.
12.2 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 Γ9 ×(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 β=0∘ -- 12.7.2.2 Trough Solution: T1 ×Γ7: β≈100.893∘ -- 12.7.2.3 Trough Solution: T2 ×Γ6: β≈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.
G Topological Graph Theory -- Contents -- G.1 Graphs -- G.2 Rings -- G.3 Faces -- References -- Compound Index -- Subject Index.
Record Nr. UNISA-996490344903316
Ceulemans Arnout  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
The theory of the Jahn-Teller effect : when a boson meets a fermion / / Arnout Ceulemans
The theory of the Jahn-Teller effect : when a boson meets a fermion / / Arnout Ceulemans
Autore Ceulemans Arnout
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (429 pages)
Disciplina 530.143
Soggetto topico Interacting boson-fermion models
Jahn-Teller effect
Efecte Jahn-Teller
Bosons
Fermions
Soggetto genere / forma Llibres electrònics
ISBN 9783031095283
9783031095276
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- 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.
4.4.3 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 Γ8 ×(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 Γ8 ×(e+t2) Dynamic Equations -- 6.6 The Γ8 ×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 ν> -- 4 -- 8.6 The Ansatz: Vibronic (12,12) Levels -- 8.7 Icosahedral Symmetry Lowering.
8.8 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 Γ9 ×(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 Γ8 ×t2g Hamiltonian -- 11.3.2 The Γ8 ×(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 Λ Irrep -- 12.1.3.2 More than One Λ Irrep -- 12.1.3.3 Illustration: The Γ×(Λ1+Λ2) Problem.
12.2 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 Γ9 ×(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 β=0∘ -- 12.7.2.2 Trough Solution: T1 ×Γ7: β≈100.893∘ -- 12.7.2.3 Trough Solution: T2 ×Γ6: β≈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.
G Topological Graph Theory -- Contents -- G.1 Graphs -- G.2 Rings -- G.3 Faces -- References -- Compound Index -- Subject Index.
Record Nr. UNINA-9910616384203321
Ceulemans Arnout  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui