Book Review
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Book Information:
Authors:
P. Exner and
H. Kovařík
Title:
Quantum waveguides
Additional book information:
Theoretical and Mathematical Physics,
Springer,
Cham,
2015,
ISBN 978-3-319-18575-0,
US$149.99 (hardcover);
ISBN 978-3-319-36556-5,
US$129.99 (softcover);
xxii+382 pp.,
ISBN 978-3-319-18576-7,
US$99.00 (e-book)
C. W. J. Beenakker and H. van Houten, Quantum transport in semiconductor nanostructures, Solid State Physics, 44 (1991) 1–228.
Gregory Berkolaiko and Peter Kuchment, Introduction to quantum graphs, Mathematical Surveys and Monographs, vol. 186, American Mathematical Society, Providence, RI, 2013. MR 3013208, DOI 10.1090/surv/186
Jiří Blank, Pavel Exner, and Miloslav Havlíček, Hilbert space operators in quantum physics, AIP Series in Computational and Applied Mathematical Physics, American Institute of Physics, New York, 1994. MR 1275370
Guy Bouchitté, M. Luísa Mascarenhas, and Luís Trabucho, On the curvature and torsion effects in one dimensional waveguides, ESAIM Control Optim. Calc. Var. 13 (2007), no. 4, 793–808. MR 2351404, DOI 10.1051/cocv:2007042
J. P. Carini, J. T. Londergan, J. T. Mullen, and D. P. Murdock, Bound states and resonances in quantum wires, Phys. Rev. B 46 (1992) 15538–15541.
J. P. Carini, J. T. Londergan, J. T. Mullen, and D. P. Murdock, Multiple bound states in sharply bent waveguides, Phys. Rev. B 48 (1993) 4503–4514.
Iain J. Clark and Anthony J. Bracken, Effective potentials of quantum strip waveguides and their dependence upon torsion, J. Phys. A 29 (1996), no. 2, 339–348. MR 1381564, DOI 10.1088/0305-4470/29/2/014
P. Exner and P. Šeba, Bound states in curved quantum waveguides, J. Math. Phys. 30 (1989), no. 11, 2574–2580. MR 1019002, DOI 10.1063/1.528538
P. Exner and P. Šeba, Trapping modes in a curved electromagnetic waveguide with perfectly conducting walls, Phys. Lett. A 144 (1990), no. 6-7, 347–350. MR 1045130, DOI 10.1016/0375-9601(90)90138-E
Richard Froese and Ira Herbst, Realizing holonomic constraints in classical and quantum mechanics, Comm. Math. Phys. 220 (2001), no. 3, 489–535. MR 1843773, DOI 10.1007/s002200100454
I. M. Glazman, Direct methods of qualitative spectral analysis of singular differential operators, Israel Program for Scientific Translations, Jerusalem, 1965; Daniel Davey & Co., Inc., New York, 1966. Translated from the Russian by the IPST staff. MR 0190800
J. Goldstone and R. L. Jaffe, Bound states in twisting tubes, Phys. Rev. B 45 (1992) 14100–14107.
Daniel Grieser, Thin tubes in mathematical physics, global analysis and spectral geometry, Analysis on graphs and its applications, Proc. Sympos. Pure Math., vol. 77, Amer. Math. Soc., Providence, RI, 2008, pp. 565–593. MR 2459891, DOI 10.1090/pspum/077/2459891
Mark Kac, Can one hear the shape of a drum?, Amer. Math. Monthly 73 (1966), no. 4, 1–23. MR 201237, DOI 10.2307/2313748
D. Krejčiřík, “Twisting versus bending in quantum waveguides”, in Analysis on Graphs and Applications (P. Exner J. P. Keating, P. Kuchment, T. Sunada, and A. Teplyaev, eds.), Proc. Sympos. Pure Math., 77 (pp. 617–636), American Mathematical Society, Providence, RI, 2008.
Christopher Lin and Zhiqin Lu, On the discrete spectrum of generalized quantum tubes, Comm. Partial Differential Equations 31 (2006), no. 10-12, 1529–1546. MR 2273964, DOI 10.1080/03605300600635111
Christopher Lin and Zhiqin Lu, Existence of bound states for layers built over hypersurfaces in $\Bbb R^{n+1}$, J. Funct. Anal. 244 (2007), no. 1, 1–25. MR 2294473, DOI 10.1016/j.jfa.2006.11.017
Christopher Lin and Zhiqin Lu, Quantum layers over surfaces ruled outside a compact set, J. Math. Phys. 48 (2007), no. 5, 053522, 14. MR 2329884, DOI 10.1063/1.2736518
John William Strutt Rayleigh Baron, The Theory of Sound, Dover Publications, New York, N.Y., 1945. 2d ed. MR 0016009
J. W. Strutt, 3rd Baron Rayleigh, On the passage of electric waves through tubes, or the vibrations of dielectric cylinders, Phil. Mag., London, 43 (261) (1897) 125–132. doi:10.1080/14786449708620969
K. Ruedenbeerg and C. W. Scherr, Free-electron network for conjugated systems. I, J. Chem. Phys. 21 (1953) 1565-1581.
Uzy Smilansky and Michael Solomyak, The quantum graph as a limit of a network of physical wires, Quantum graphs and their applications, Contemp. Math., vol. 415, Amer. Math. Soc., Providence, RI, 2006, pp. 283–291. MR 2277623, DOI 10.1090/conm/415/07875
W. Thirring, A course in mathematical physics, III: Quantum mechanics of atoms and molecules, Springer-Verlag, New York and Vienna, 1981.
Jakob Wachsmuth and Stefan Teufel, Effective Hamiltonians for constrained quantum systems, Mem. Amer. Math. Soc. 230 (2014), no. 1083, vi+83. MR 3236129
Andrew Zangwill, Modern electrodynamics, Cambridge University Press, Cambridge, 2013. MR 3012344
References
- C. W. J. Beenakker and H. van Houten, Quantum transport in semiconductor nanostructures, Solid State Physics, 44 (1991) 1–228.
- Gregory Berkolaiko and Peter Kuchment, Introduction to quantum graphs, Mathematical Surveys and Monographs, vol. 186, American Mathematical Society, Providence, RI, 2013. MR 3013208
- JiříBlank, Pavel Exner, and Miloslav Havlíček, Hilbert space operators in quantum physics, AIP Series in Computational and Applied Mathematical Physics, American Institute of Physics, New York, 1994. MR 1275370
- Guy Bouchitté, M. Luísa Mascarenhas, and Luís Trabucho, On the curvature and torsion effects in one dimensional waveguides, ESAIM Control Optim. Calc. Var. 13 (2007), no. 4, 793–808. MR 2351404
- J. P. Carini, J. T. Londergan, J. T. Mullen, and D. P. Murdock, Bound states and resonances in quantum wires, Phys. Rev. B 46 (1992) 15538–15541.
- J. P. Carini, J. T. Londergan, J. T. Mullen, and D. P. Murdock, Multiple bound states in sharply bent waveguides, Phys. Rev. B 48 (1993) 4503–4514.
- Iain J. Clark and Anthony J. Bracken, Effective potentials of quantum strip waveguides and their dependence upon torsion, J. Phys. A 29 (1996), no. 2, 339–348. MR 1381564
- P. Exner and P. Šeba, Bound states in curved quantum waveguides, J. Math. Phys. 30 (1989), no. 11, 2574–2580. MR 1019002
- P. Exner and P. Šeba, Trapping modes in a curved electromagnetic waveguide with perfectly conducting walls, Phys. Lett. A 144 (1990), no. 6-7, 347–350. MR 1045130
- Richard Froese and Ira Herbst, Realizing holonomic constraints in classical and quantum mechanics, Comm. Math. Phys. 220 (2001), no. 3, 489–535. MR 1843773
- I. M. Glazman, Direct methods of qualitative spectral analysis of singular differential operators, Translated from the Russian by the IPST staff, Israel Program for Scientific Translations, Jerusalem, 1965; Daniel Davey & Co., Inc., New York, 1966. MR 0190800
- J. Goldstone and R. L. Jaffe, Bound states in twisting tubes, Phys. Rev. B 45 (1992) 14100–14107.
- Daniel Grieser, Thin tubes in mathematical physics, global analysis and spectral geometry, Analysis on graphs and its applications, Proc. Sympos. Pure Math., vol. 77, Amer. Math. Soc., Providence, RI, 2008, pp. 565–593. MR 2459891
- Mark Kac, Can one hear the shape of a drum?, Amer. Math. Monthly 73 (1966), no. 4, 1–23. MR 0201237
- D. Krejčiřík, “Twisting versus bending in quantum waveguides”, in Analysis on Graphs and Applications (P. Exner J. P. Keating, P. Kuchment, T. Sunada, and A. Teplyaev, eds.), Proc. Sympos. Pure Math., 77 (pp. 617–636), American Mathematical Society, Providence, RI, 2008.
- Christopher Lin and Zhiqin Lu, On the discrete spectrum of generalized quantum tubes, Comm. Partial Differential Equations 31 (2006), no. 10-12, 1529–1546. MR 2273964
- Christopher Lin and Zhiqin Lu, Existence of bound states for layers built over hypersurfaces in $\mathbb {R}^{n+1}$, J. Funct. Anal. 244 (2007), no. 1, 1–25. MR 2294473
- Christopher Lin and Zhiqin Lu, Quantum layers over surfaces ruled outside a compact set, J. Math. Phys. 48 (2007), no. 5, 053522, 14. MR 2329884
- J. W. Strutt, 3rd Baron Rayleigh, The theory of sound, second edition, Dover, New York, 1945 (original publication, 1894). MR 0016009
- J. W. Strutt, 3rd Baron Rayleigh, On the passage of electric waves through tubes, or the vibrations of dielectric cylinders, Phil. Mag., London, 43 (261) (1897) 125–132. doi:10.1080/14786449708620969
- K. Ruedenbeerg and C. W. Scherr, Free-electron network for conjugated systems. I, J. Chem. Phys. 21 (1953) 1565-1581.
- Uzy Smilansky and Michael Solomyak, The quantum graph as a limit of a network of physical wires, Quantum graphs and their applications, Contemp. Math., vol. 415, Amer. Math. Soc., Providence, RI, 2006, pp. 283–291. MR 2277623
- W. Thirring, A course in mathematical physics, III: Quantum mechanics of atoms and molecules, Springer-Verlag, New York and Vienna, 1981.
- Jakob Wachsmuth and Stefan Teufel, Effective Hamiltonians for constrained quantum systems, Mem. Amer. Math. Soc. 230 (2014), no. 1083, vi+83. MR 3236129
- Andrew Zangwill, Modern electrodynamics, Cambridge University Press, Cambridge, 2013. MR 3012344
Review Information:
Reviewer:
Evans M. Harrell II
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta Georgia 30332-0160
Email:
harrell@math.gatech.edu
Journal:
Bull. Amer. Math. Soc.
55 (2018), 321-324
DOI:
https://doi.org/10.1090/bull/1604
Published electronically:
December 15, 2017
Review copyright:
© Copyright 2017
Evans M. Harrell II, with fair use permitted.
