Nodal domains on isospectral quantum graphs: The resolution of isospectrality?

Journal of Physics A: Mathematical and General

Volumn 39, Issue 45, 2006, Pages 13999-14014

  Band, Ram ^a   Shapira, Talia ^a   Smilansky, Uzy ^a,b  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33947155537     PISSN: 03054470     EISSN: 13616447     Source Type: Journal    
DOI: 10.1088/0305-4470/39/45/009     Document Type: Article

References (29)

1. Gordon C, Webb D and Wolpert S 1992 Bull. Am. Math. Soc. 27 134-8
2. Chapman S 1995 Am. Math. Mon. 102 124
3. Buser P, Conway J, Doyle P and Semmler K-D 1994 Int. Math. Res. Not. 9 391-400
4. Okada Y and Shudo A 2001 J. Phys. A: Math. Gen. 34 5911-22
5. Jakobson D, Levitin M, Nadirashvili N and Polterovich I 2006 J. Comput. Appl. Math. 194 141-55
6. Levitin M, Parnovski L and Polterovich I 2006 J. Phys. A: Math. Gen. 39 2073-82
7. Sunada T 1985 Ann. Math. 121 196-86
8. Kac M 1966 Am. Math. Mon. 73 1-23
9. Milnor J 1964 Proc. Natl Acad. Sci. USA 51 542
10. Brüning J 1978 Math. Z. 158 15
11. Zelditch S 1998 J. Differ. Geom. 49 207
12. Zelditch S 2004 Surveys in differential geometry IX 401-67
13. Fisher M E 1966 J. Comb. Theory 1 105-25
14. Gutkin B and Smilansky U 2001 J. Phys A.: Math. Gen. 31 6061-8
15. Brooks R 1999 Ann. Inst. Fouriere 49 707-25
16. von Below J 2000 Partial Differential Equations on Multistructeres (Lecture Notes in Pure and Applied Mathematics vol 219) (New York: Dekker) pp 19-36
17. Carlson R 1999 Trans. Am. Math. Soc. 351 4069-88
18. Blum G, Gnutzmann S and Smilansky U 2002 Phys. Rev. Lett. 88 114101
19. Roth J-P Lectures Notes in Mathematics: Theorie du Potentiel ed A Dold and B Eckmann (Berlin: Springer) pp 521-39
20. Kottos T and Smilansky U 1999 Ann. Phys., NY 274 76
21. Gnutzmann S, Smilansky U and Sondergaard N 2005 J. Phys. A: Math. Gen. 38 8921-33
22. Shapira Talia and Smilansky Uzy 2004 Proceedings of the NATO Advanced Research Workshop (Tashkent, Uzbekistan, 2004) at press
23. Gnutzman S, Smilansky U and Weber J 2004 Waves Random Media 14 S61-73
24. Schapotschnikow P 2006 Waves Complex Random Media 16 167-78
25. Berkolaiko G 2006 Private communication
26. Davies E B, Leydold J and Stadler P F 2001 Linear Alegbra Appl. 336 51
27. Barra F and Gaspard P 2000 J. Stat. Phys. 101 283
28. Courant R and Hilbert D 1953 Methods of Mathematical Physics vol 1 (New York: Interscience) pp 451-65
29. Gnutzmann S, Karageorge P D and Smilansky U 2006 Phys. Rev. Lett. 97 090201