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2011 | 120 | 6A | A-149-A-153
Article title

Note on the Role of Symmetry in Scattering from Isospectral Graphs and Drums

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EN
Abstracts
EN
We discuss scattering from pairs of isospectral quantum graphs constructed using the method described in the papers of Parzanchevski, Band and Ben-Shach. It was shown in the paper of Band et al. that scattering matrices of such graphs have the same spectrum and polar structure, provided that infinite leads are attached in a way which preserves the symmetry of isospectral construction. In the current paper we compare this result with the conjecture put forward by Okada et al. that the pole distribution of scattering matrices in the exterior of isospectral domains in ℝ^{2} is different.
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Year
Volume
120
Issue
6A
Pages
A-149-A-153
Physical description
Dates
published
2011-12
Contributors
author
  • School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
  • Department of Physics of Complex Systems, the Weizmann Institute of Science, Rehovot 76100, Israel
author
  • School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
  • Center for Theoretical Physics, Polish Academy of Sciences, al. Lotników 32/46,02-668 Warszawa, Poland
author
  • Department of Physics of Complex Systems, the Weizmann Institute of Science, Rehovot 76100, Israel
  • Cardiff School of Mathematics and WIMCS, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, UK
References
  • [1] M. Kac, Am. Math. Mon. 73, 1 (1966)
  • [2] T. Sunada, Ann. Math. 121, 169 (1985)
  • [3] C. Gordon, D. Webb, S. Wolpert, Bull. Am. Math. Soc. 27, 134 (1992)
  • [4] C. Gordon, D. Webb, S. Wolpert, Invent. Math. 110, 1 (1992)
  • [5] P. Berard, Math. Ann. 292, 547 (1992)
  • [6] Z. Steven, Comm. Partial Diff. Equations 17, 221 (1992)
  • [7] L. Guillope, M. Zworski, Ann. Math. 145, 597 (1997)
  • [8] R. Brooks, O. Davidovich, Isoscattering on Surfaces, 2002
  • [9] C. Gordon, P. Perry, D. Schueth, Contemp. Math. 387, 157 (2005)
  • [10] C. Gordon, Contemp. Math. 484, 45 (2009)
  • [11] R. Brooks, Contemp. Math. 231, 25 (1999)
  • [12] B. Gutkin, U. Smilansky, J. Phys. A 34, 6061 (2001)
  • [13] R. Band, O. Parzanchevski, G. Ben-Shach, J. Phys. A, Math. Theor. 42, 175202 (2009)
  • [14] O. Parzanchevski, R. Band, J. Geometr. Anal. 20, 439 (2010)
  • [15] R. Band, A. Sawicki, U. Smilansky, J. Phys. A Math. Theor. 43, 415201 (2010)
  • [16] Y. Okada, A. Shudo, S. Tasaki, T. Harayama, J. Phys. A, Math. Gen. 38, L163 (2005)
  • [17] P. Buser, J. Conway, P. Doyle, K.-D. Semmler, Int. Math. Res. Not. 9, 391 (1994)
  • [18] S. Gnutzmann, U. Smilansky, Adv. Phys. 55, 527 (2006)
  • [19] P. Kuchment, Waves Random Media 14, S107 (2004)
  • [20] R. Band, G. Berkolaiko, U. Smilansky, Dynamics of nodal points and the nodal count on a family of quantum graphs, in: Ann. Henri Poincaré (2011), http://dx.doi.org/10.1007/s00023-011-0124-1
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.bwnjournal-article-appv120n6ap60kz
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