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Quantum Chaos and Mesoscopic Systems

Mathematical Methods in the Quantum Signatures of Chaos

  • Book
  • © 1997

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Authors:
  1. Norman E. Hurt

    1. Zeta Associates, Fairfax, USA

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

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xv
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  2. Signatures of Quantum Chaos

    • Norman E. Hurt
    Pages 1-70

  3. Billiards: Polygonal and Others

    • Norman E. Hurt
    Pages 71-88

  4. Quantum Transition Amplitudes

    • Norman E. Hurt
    Pages 89-124

  5. Variance of Quantum Matrix Elements

    • Norman E. Hurt
    Pages 125-132

  6. Error Terms

    • Norman E. Hurt
    Pages 133-140

  7. Co-Finite Model for Quantum Chaology

    • Norman E. Hurt
    Pages 141-152

  8. Landau Levels and L-Functions

    • Norman E. Hurt
    Pages 153-178

  9. Wigner Time Delay

    • Norman E. Hurt
    Pages 179-196

  10. Scattering Theory for Leaky Tori

    • Norman E. Hurt
    Pages 197-210

  11. Dissolving Bound States

    • Norman E. Hurt
    Pages 211-226

  12. Dissolving Eigenvalues

    • Norman E. Hurt
    Pages 227-234

  13. Half-Integral Forms

    • Norman E. Hurt
    Pages 235-252

  14. Isometric and Isospectral Manifolds

    • Norman E. Hurt
    Pages 253-262

  15. Mesoscopic Structures

    • Norman E. Hurt
    Pages 263-296

  16. References

    • Norman E. Hurt
    Pages 297-328

  17. Back Matter

    Pages 329-335
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Keywords

About this book

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.

Authors and Affiliations

  • Zeta Associates, Fairfax, USA

    Norman E. Hurt

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