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Quantum Chaos and Mesoscopic Systems - N.E. Hurt

Quantum Chaos and Mesoscopic Systems

Mathematical Methods in the Quantum Signatures of Chaos

(Autor)

Buch | Hardcover
336 Seiten
1997
Springer (Verlag)
978-0-7923-4459-9 (ISBN)
CHF 299,55 inkl. MwSt
4 Nonhyperbolic Case . . . . . . . 5 Random Matrix Theory . . . . . 7 Appendix: Baker's Map . . . 3 Form Factor for Primes . 5 Binary Quadratic Forms as a Model . 2 Co-finite Models . 8 Equidistribution Theory . 4 Selberg's Spectral Theorem . 5 Pseudo Billiards . 7 Automorphic Forms . 10 Hecke Operators . 12 Eigenvalue Statistics on X .
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.

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.

Reihe/Serie Mathematics and Its Applications ; 397
Mathematics and Its Applications ; 397
Zusatzinfo XVI, 336 p.
Verlagsort Dordrecht
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Angewandte Mathematik
Naturwissenschaften Physik / Astronomie Quantenphysik
ISBN-10 0-7923-4459-6 / 0792344596
ISBN-13 978-0-7923-4459-9 / 9780792344599
Zustand Neuware
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