On the accuracy of the semiclassical trace formula

Journal of Physics A: Mathematical and General

Volumn 31, Issue 29, 1998, Pages 6253-6277

  Primack, Harel ^a,b   Smilansky, Uzy ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032563036     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/31/29/016     Document Type: Article

References (41)

1. Gutzwiller M C 1990 Chaos in Classical and Quantum Mechanics. (New York: Springer)
2. Berry M V 1985 Semiclassical theory of spectral rigidity Proc. R. Soc. A 400 229
3. Bogomolny E B and Keating J P 1996 Gutzwiller's trace formula and spectral statistics: beyond the diagonal approximation Phys. Rev. Lett. 77 1472-5
4. Landau L D and Lifshitz E M 1958 Quantum mechanics, non-relativistic theory Course of Theoretical Physics vol 3 (Oxford: Pergamon)
5. Pauli W 1951 Ausgewählte Kapital aus der Feldquantisierung (Lecture Notes) ed C Enz (Zürich)
6. Primack H and Smilansky U 1995 Quantization of the three-dimensional Sinai billiard Phys. Rev. Lett. 74 4831-4
7. Primack H 1997 Quantal and semiclassical analysis of the three-dimensional Sinai billiard PhD Thesis The Weizmann Institute of Science, Rehovot, Israel
8. Prosen T 1997 Quantization of generic chaotic 3d billiard with smooth boundary I: energy level statistics Phys. Lett. A 233 323-31
9. Gutzwiller M C 1991 The semi-classical quantization of chaotic hamiltonian systems Proc. 1989 Les Houches Summer School on 'Chaos and Quantum Physics' ed M-J Giannoni, A Voros and J Zinn-Justin (Amsterdam: Elsevier) pp 201-49
10. Gaspard P and Alonso D 1993 ℏ expansion for the periodic orbit quantization of hyperbolic systems Phys. Rev. A 47 R3468-71
11. Alonso D and Gaspard P 1993 ℏ expansion for the periodic orbit quantization of chaotic systems Chaos 3 601-12
12. Vattay G, Wirzba A and Rosenqvist P E 1994 Periodic orbit theory of diffraction Phys. Rev. Lett. 73 2304
13. Primack H, Schanz H, Smilansky U and Ussishkin I 1997 Penumbra diffraction in the semiclassical quantization of concave billiards J. Phys. A: Math. Gen. 30 6693-723
14. Boasman P A 1994 Semiclassical accuracy for billiards Nonlinearity 7 485-533
15. Berry M V and Wilkinson M 1984 Diabolical points in the spectra of triangles Proc. R. Soc. A 392 15-43
16. Bleher P M 1991 Quasi-classical expansions and the problem of quantum chaos Geometric Aspects of Functional Analysis, Proc. Israel Semin., GAFA, Israel 1989-90 (Lecture Notes in Mathematics) (Berlin: Springer) pp 60-89
17. Bleher P M 1994 Distribution of energy levels of a quantum free particle on a surface of revolution Duke Math. J. 74 45-93
18. Prosen T and Robnik M 1993 Failure of semiclassical methods to predict individual energy levels J. Phys. A: Math. Gen. 16 L37-44
19. Aurich R and Marklof J 1996 Trace formulae for three-dimensional hyperbolic lattice and application to a strongly chaotic tetrahedral billiard Physica 92D 101-29
20. Keating J P 1993 The Riemann zeta function and quantum chaology Proc. 1991 Enrico Fermi International School on 'Quantum Chaos' course CXIX, ed G Casati, I Guarnery and U Smilansky (Amsterdam: NorthHolland)
21. Balian R and Bloch B 1970 Distribution of eigenfrequencies for the wave equation in a finite domain I. Three-dimensional problem with smooth boundary surface Ann. Phys. 60 401-47
22. Baltes H P and Hilf E R 1976 Spectra of Finite Systems (Mannheim: Bibliographisches Institut)
23. Berry M V and Howls C J 1994 High orders of the Weyl expansion for quantum billiards: resurgence of the Weyl series, and the Stokes phenomenon Proc. R. Soc. A 447 527-55
24. Doron E and Smilansky U 1992 Semiclassical quantization of chaotic billiards - a scattering theory approach Nonlinearity 5 1055-84
25. Bogomolny E B 1992 Semiclassical quantization of multidimensional systems Nonlinearity 5 805
26. Georgeot B and Prange R E 1995 Exact and quasiclassical Fredholm solutions of quantum billiards Phys. Rev. Lett. 74 2851-4
27. Sieber M 1991 The hyperbola billiard: a model for the semiclassical quantization of chaotic systems PhD Thesis University of Hamburg, DESY report 91-030
28. Harayama T and Shudo A 1992 Periodic orbits and semiclassical quantization of dispersing billiards J. Phys. A: Math. Gen. 25 4595-611
29. Berry M V 1991 Some quantum to classical asymptolics Proc. 1989 Les Hauches Summer School on 'Chaos and Quantum Physics' ed M-J Giannoni, A Voros and J Zinn-Justin (Amsterdam: Elsevier) p 251
30. Andersson K G and Melrose R B 1977 The propagation of singularities ilong gliding rays Inv. Math. 41 197-232
31. Bohigas O, Giannoni M J and Schmit C 1984 Characterization of chaotic quantum spectra and universality of level fluctuations Phys. Rev. Lett. 52 1-4
32. Schanz H and Smilansky U 1995 Quantization of Sinai's billiard - a scattering approach Chaos, Solitons and Fractals 5 1289-309
33. Schanz H 1997 Investigation of two quantum chaotic systems PhD Thesis Humboldt University Berlin (Berlin: LOGOS)
34. Primack H, Schanz H, Smilansky U and Ussishkin I 1996 Penumbra diffraction in the quantization of dispersing billiards Phys. Rev. Lett. 76 1615-18
35. Fendrik A J and Sanchez M J 1995 Decay of the Sinai well in d dimensions Phys. Rev. E 51 2996
36. Dahlqvist P and Artuso R 1996 On the decay of correlations in Sinai billiards with infinite horizon Phys. Lett. A 219 212-16
37. Berry M V 1981 Quantizing a classically ergodic system: Sinai billiard and the KKR method Ann. Phys. 131 163-216
38. Sieber M, Smilansky U, Creagh S C and Littlejohn R G 1993 Non-generic spectral statistics in the quantized stadium billiard J. Phys. A: Math. Gen. 26 6217-30
39. Sieber M, Primack H, Smilansky U, Ussishkin I and Schanz H 1995 Semiclassical quantization of billiards with mixed boundary conditions J. Phys. A: Math. Gen. 28 5041-78
40. Bogomolny E and Schmit C 1993 Semiclassical computations of energy levels Nonlinearity 6 523-47
41. Aurich R, Bolte J and Steiner F 1994 Universal signatures of quantum chaos Phys. Rev. Lett. 73 1356-9