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Quantum Chaos and Mesoscopic Systems

Mathematical Methods in the Quantum Signatures of Chaos

  • Norman E. Hurt

Part of the Mathematics and Its Applications book series (MAIA, volume 397)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Norman E. Hurt
    Pages 1-70
  3. Norman E. Hurt
    Pages 71-88
  4. Norman E. Hurt
    Pages 89-124
  5. Norman E. Hurt
    Pages 125-132
  6. Norman E. Hurt
    Pages 133-140
  7. Norman E. Hurt
    Pages 141-152
  8. Norman E. Hurt
    Pages 153-178
  9. Norman E. Hurt
    Pages 179-196
  10. Norman E. Hurt
    Pages 197-210
  11. Norman E. Hurt
    Pages 211-226
  12. Norman E. Hurt
    Pages 227-234
  13. Norman E. Hurt
    Pages 235-252
  14. Norman E. Hurt
    Pages 253-262
  15. Norman E. Hurt
    Pages 263-296
  16. Norman E. Hurt
    Pages 297-328
  17. Back Matter
    Pages 329-335

About this book

Introduction

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.

Keywords

Signatur manifold number theory quantum chaos scattering theory

Authors and affiliations

  • Norman E. Hurt
    • 1
  1. 1.Zeta AssociatesFairfaxUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-8792-1
  • Copyright Information Springer Science+Business Media B.V. 1997
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4811-0
  • Online ISBN 978-94-015-8792-1
  • Buy this book on publisher's site
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