عنوان

Quantum Chaos and Mesoscopic Systems

9789048148110

9789401587921

b408377

Quantum Chaos and Mesoscopic Systems

[Book]

Mathematical Methods in the Quantum Signatures of Chaos /

by Norman E. Hurt.

Dordrecht :

Imprint: Springer,

1997.

Mathematics and Its Applications ;

397

1 Signatures of Quantum Chaos -- 2 Billiards: Polygonal and Others -- 3 Quantum Transition Amplitudes -- 4 Variance of Quantum Matrix Elements -- 5 Error Terms -- 6 Co-Finite Model for Quantum Chaology -- 7 Landau Levels and L-Functions -- 8 Wigner Time Delay -- 9 Scattering Theory for Leaky Tori -- 10 Dissolving Bound States -- 11 Dissolving Eigenvalues -- 12 Half-Integral Forms -- 13 Isometric and Isospectral Manifolds -- 14 Mesoscopic Structures -- 15 References.

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4. 2 Variance of Quantum Matrix Elements. 125 4. 3 Berry's Trick and the Hyperbolic Case 126 4. 4 Nonhyperbolic Case . . . . . . . 128 4. 5 Random Matrix Theory . . . . . 128 4. 6 Baker's Map and Other Systems 129 4. 7 Appendix: Baker's Map . . . . . 129 5 Error Terms 133 5. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . 133 5. 2 The Riemann Zeta Function in Periodic Orbit Theory 135 5. 3 Form Factor for Primes . . . . . . . . . . . . . . . . . 137 5. 4 Error Terms in Periodic Orbit Theory: Co-compact Case. 138 5. 5 Binary Quadratic Forms as a Model . . . . . . . . . . . . 139 6 Co-Finite Model for Quantum Chaology 141 6. 1 Introduction. . . . . . . . 141 6. 2 Co-finite Models . . . . . 141 6. 3 Geodesic Triangle Spaces 144 6. 4 L-Functions. . . . . . . . 145 6. 5 Zelditch's Prime Geodesic Theorem. 146 6. 6 Zelditch's Pseudo Differential Operators 147 6. 7 Weyl's Law Generalized 148 6. 8 Equidistribution Theory . . . . . . . . . 150 7 Landau Levels and L-Functions 153 7. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . 153 7. 2 Landau Model: Mechanics on the Plane and Sphere. 153 7. 3 Landau Model: Mechanics on the Half-Plane 155 7. 4 Selberg's Spectral Theorem . . . . . . . . . . . 157 7. 5 Pseudo Billiards . . . . . . . . . . . . . . . . . 158 7. 6 Landau Levels on a Compact Riemann Surface 159 7. 7 Automorphic Forms . . . . . 160 7. 8 Maass-Selberg Trace Formula 162 7. 9 Degeneracy by Selberg. . . . 163 7. 10 Hecke Operators . . . . . . . 163 7. 11 Selberg Trace Formula for Hecke Operators 167 7. 12 Eigenvalue Statistics on X . . . . 169 7. 13 Mesoscopic Devices. . . . . . . . 170 7. 14 Hall Conductance on Leaky Tori 170 7.

9789048148110

Springer eBooks

Global analysis.

Mathematics.

Number theory.

Quantum theory.

Hurt, Norman E.

SpringerLink (Online service)

20190307161400.0

[Book]

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