Book Review
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MathSciNet review:
3196800
Full text of review:
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Book Information:
Authors:
Gregory Berkolaiko and
Peter Kuchment
Title:
Introduction to quantum graphs
Additional book information:
Mathematical Surveys and Monographs, vol.~186,
American Mathematical Society,
Providence, RI,
2013,
xiii+270 pp.,
ISBN 978-0-8218-9211-4,
US $86.00
Pavel Exner, Jonathan P. Keating, Peter Kuchment, Toshikazu Sunada, and Alexander Teplyaev (eds.), Analysis on graphs and its applications, Proceedings of Symposia in Pure Mathematics, vol. 77, American Mathematical Society, Providence, RI, 2008. Papers from the program held in Cambridge, January 8–June 29, 2007. MR 2459860, DOI 10.1090/pspum/077
P. Exner and P. Šeba, Free quantum motion on a branching graph, Rep. Math. Phys. 28 (1989), no. 1, 7–26. MR 1109248, DOI 10.1016/0034-4877(89)90023-2
V. Kostrykin and R. Schrader, Kirchhoff’s rule for quantum wires, J. Phys. A 32 (1999), no. 4, 595–630. MR 1671833, DOI 10.1088/0305-4470/32/4/006
T. Kottos and U. Smilansky, Quantum chaos on graphs, Phys. Rev. Lett. 79 (1997), 4794-4797.
Peter Kuchment, Quantum graphs. I. Some basic structures, Waves Random Media 14 (2004), no. 1, S107–S128. Special section on quantum graphs. MR 2042548, DOI 10.1088/0959-7174/14/1/014
Peter Kuchment, Quantum graphs. II. Some spectral properties of quantum and combinatorial graphs, J. Phys. A 38 (2005), no. 22, 4887–4900. MR 2148631, DOI 10.1088/0305-4470/38/22/013
N. I. Gerasimenko and B. S. Pavlov, A scattering problem on noncompact graphs, Teoret. Mat. Fiz. 74 (1988), no. 3, 345–359 (Russian, with English summary); English transl., Theoret. and Math. Phys. 74 (1988), no. 3, 230–240. MR 953298, DOI 10.1007/BF01016616
Jean-Pierre Roth, Spectre du laplacien sur un graphe, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), no. 19, 793–795 (French, with English summary). MR 711833
K. Ruedenberg and C. W. Scherr, Free-electron network model for conjugated systems, I. Theory, J. Chem. Phys. 21 (1953), 1565-1581.
References
- P. Exner, J. P. Keating, P. Kuchment, T. Sunada, A. Teplayaev, Editors, Analysis on graphs and its applications, Papers from the program held in Cambridge, January 8–June 29, 2007, Proc. Symp. Pure Math., vol. 77; Amer. Math. Soc., Providence, R.I., 2008. MR 2459860 (2009i:00008)
- P. Exner and P. Šeba, Free quantum motion on a branching graph, Rep. Math. Phys. 28 (1989), no. 1, 7–26. MR 1109248 (92e:81019), DOI 10.1016/0034-4877(89)90023-2
- V. Kostrykin and R. Schrader, Kirchhoff’s rule for quantum wires, J. Phys. A 32 (1999), no. 4, 595–630. MR 1671833 (99m:81280), DOI 10.1088/0305-4470/32/4/006
- T. Kottos and U. Smilansky, Quantum chaos on graphs, Phys. Rev. Lett. 79 (1997), 4794-4797.
- Peter Kuchment, Quantum graphs. I. Some basic structures, Waves Random Media 14 (2004), no. 1, S107–S128. Special section on quantum graphs. MR 2042548 (2005h:81148), DOI 10.1088/0959-7174/14/1/014
- Peter Kuchment, Quantum graphs. II. Some spectral properties of quantum and combinatorial graphs, J. Phys. A 38 (2005), no. 22, 4887–4900. MR 2148631 (2006a:81035), DOI 10.1088/0305-4470/38/22/013
- N. I. Gerasimenko and B. S. Pavlov, A scattering problem on noncompact graphs, Teoret. Mat. Fiz. 74 (1988), no. 3, 345–359 (Russian, with English summary); English transl., Theoret. and Math. Phys. 74 (1988), no. 3, 230–240. MR 953298 (90f:47010), DOI 10.1007/BF01016616
- Jean-Pierre Roth, Spectre du laplacien sur un graphe, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), no. 19, 793–795 (French, with English summary). MR 711833 (84g:58104), DOI 10.1007/BFb0100128
- K. Ruedenberg and C. W. Scherr, Free-electron network model for conjugated systems, I. Theory, J. Chem. Phys. 21 (1953), 1565-1581.
Review Information:
Reviewer:
Pavel Exner
Affiliation:
Czech Academy of Sciences
Email:
exner@ujf.cas.cz
Journal:
Bull. Amer. Math. Soc.
51 (2014), 511-514
DOI:
https://doi.org/10.1090/S0273-0979-2014-01449-1
Published electronically:
January 13, 2014
Review copyright:
© Copyright 2014
American Mathematical Society
