Quantum Chaos and Mesoscopic Systems: Mathematical Methods in the Quantum Signatures of Chaos

ISBN-13: 9789048148110 / Angielski / Miękka / 2010 / 336 str.

N. E. Hurt

Opis

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.

Spis treści

Preface. 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. Index.