Quantum Chaos and Mesoscopic Systems

Mathematical Methods in the Quantum Signatures of Chaos
1. Auflage. Softcover version of original hardcover Auflage 1997
ISBN: 978-90-481-4811-0
Verlag: Springer Netherlands

Buch, Englisch, 336 Seiten, Previously published in hardcover, Format (B × H): 170 mm x 244 mm, Gewicht: 615 g

Reihe: Mathematics and Its Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Hurt, N. E.

Fachgebiete

• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Naturwissenschaften Physik Quantenphysik

Inhaltsverzeichnis

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.