Families of Line-Graphs and Their Quantization

Journal of Statistical Physics

Volumn 111, Issue 5-6, 2003, Pages 1331-1352

  Pakoński, Prot ^a   Tanner, Gregor ^b   Życzkowski, Karol ^c  

^a JAGIELLONIAN UNIVERSITY   (Poland)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

^c CENTER FOR THEORETICAL PHYSICS   (Poland)

Author keywords

Line graph; Quantum graphs; Semiclassical limit; Spectral statistics

Indexed keywords

EID: 0345862119     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1023012502046     Document Type: Article

References (27)

1. T. Kottos and U. Smilansky, Phys. Rev. Lett. 79:4794 (1997).
2. T. Kottos and U. Smilansky, Ann. Phys. NY 274:76 (1999).
3. G. Berkolaiko and J. P. Keating, J. Phys. A: Math. Gen. 32:7814 (1999).
4. H. Schanz and U. Smilansky, Philos. Mag. B 80:1999 (2000).
5. H. Schanz and U. Smilansky, Phys. Rev. Lett. 84:1427 (2000).
6. T. Kottos and U. Smilansky, Phys. Rev. Lett. 85:968 (2000).
7. F. Barra and P. Gaspard, J. Statist. Phys. 101:283 (2000).
8. G. Berkolaiko, E. B. Bogomolny, and J. P. Keating J. Phys. A: Math. Gen. 34:335 (2001).
9. F. Barra and P. Gaspard, Phys. Rev. E 63:066215 (2001).
10. G. Berkolaiko, H. Schanz, and R. S. Whitney, Phys. Rev. Lett. 88:104101 (2002).
11. G. Tanner, J. Phys. A 35:5985 (2002).
12. G. Tanner, J. Phys. A: Math. Gen. 33:3567 (2000).
13. G. Tanner, J. Phys. A: Math. Gen. 34:8485 (2001).
14. P. Pakoński, K. Zyczkowski, and M. Kuś, J. Phys. A: Math. Gen. 34:9303 (2001).
15. D. M. Cvetković, M. Doob, and H. Sachs, Spectra of Graphs: Theory and Application, 2nd ed. (Deutscher Verlag der Wissenschaften, Berlin, 1982).
16. J. Bang-Jensen and G. Gutin, Digraphs: Theory, Algorithms and Applications (Springer, London, 2001).
17. A. Mostowski and M. Stark, Introduction to Higher Algebra (Pergamon, Oxford, 1964).
18. A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems (Cambridge University Press, Cambridge, 1995).
19. A. W. Marshall and I. Olkin, The Theory of Majorizations and Its Applications (Academic Press, New York, 1979).
20. G. Berkolaiko, J. Phys. A: Math. Gen. 34:L319 (2001).
21. K. Zyczkowski, W. Słomczyński, M. Kuś, and H.-J. Sommers, preprint Random Unistochastic Matrices nlin.CD/0112036 (2001).
22. S. Severini, preprint On the Pattern of Unitary Matrices math.CO/0205187 2002.
23. P. I. Richards, SIAM Rev. 9:548 (1967).
24. R. L. Hemminger and L. W. Beineke, in Selected Topics in Graph Theory, L. W. Beineke and R. J. Wilson, eds. (Academic Press, London, 1978), p. 271.
25. F. J. Dyson, J. Math. Phys. 3:140, 157, 166 (1962).
26. F. Haake, Quantum Signatures of Chaos, 2nd Ed. (Springer-Verlag, Berlin, 2000).
27. M. L. Mehta, Random Matrices, 2nd Ed. (Academic Press, New York, 1991).