Quantum graphs with singular two-particle interactions

Journal of Physics A: Mathematical and Theoretical

Volumn 46, Issue 4, 2013, Pages

  Bolte, Jens ^a   Kerner, Joachim ^a  

^a UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84872718969     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/46/4/045206     Document Type: Article

References (23)

1. Bolte J and Endres S 2009 The trace formula for quantum graphs with general self-adjoint boundary conditions Ann. Inst. Henri Poincare 10 189-223
2. Bohigas O, Giannoni M J and Schmit C 1984 Characterization of chaotic quantum spectra and universality of level fluctuation laws Phys. Rev. Lett. 52 1-4
3. Bolte J and Kerner J 2013 Quantum graphs with two-particle contact interactions J. Phys. A: Math. Theor. 46 045207
4. Dauge M 1988 Elliptic Boundary Value Problems on Corner Domains: Smoothness and Asymptotics of Solutions (Lecture Notes in Mathematics vol 1341) (Berlin: Springer)
5. Dobrowolski M 2005 Angewandte Funktionalanalysis: Funktionalanalysis, Sobolev-Räume und Elliptische Differentialgleichungen (Berlin: Springer)
6. Exner P, Keating J P, Kuchment P, Sunada T and Teplyaev A (ed) 2007 Analysis on Graphs and its Applications: Proceedings of Symposia in Pure Mathematics (Cambridge, 8 January-29 June) (Providence, RI: American Mathematical Society)
7. Gnutzman S and Smilansky U 2006 Quantum graphs: application to quantum chaos and universal spectral statistics Adv. Phys. 55 527-625 (Pubitemid 44773296)
8. Gilbarg D and Trudinger N S 1983 Elliptic Partial Differential Equations of Second Order (Grundlehren der Mathematischen Wissenschaften vol 224) 2nd edn (Berlin: Springer)
9. Harmer M 2007 Two particles on a star graph. I Russ. J. Math. Phys. 14 435-9
10. Harmer M 2008 Two particles on a star graph. II Russ. J. Math. Phys. 15 473-80
11. Harrison J M, Keating J P and Robbins J M 2011 Quantum statistics on graphs Proc. R. Soc. Lond. Ser. A 467 212-33
12. Karamata J 1931 Neuer Beweis und Verallgemeinerung einiger Tauberian-Sätze Math. Z. 33 294-9
13. Kato T 1966 Perturbation Theory for Linear Operators (Die Grundlehren der mathematischen Wissenschaften Band 132) (New York: Springer)
14. Kostrykin V and Schrader R 1999 Kirchhoff's rule for quantum wires J. Phys. A: Math. Gen. 32 595-630
15. Kottos T and Smilansky U 1999 Periodic orbit theory and spectral statistics for quantum graphs Ann. Phys., NY 274 76-124
16. Kuchment P 2004 Quantum graphs: I. Some basic structures Waves Random Media 14 S107-28
17. Melnikov Yu B and Pavlov B S 1995 Two-body scattering on a graph and application to simple nanoelectronic devices J. Math. Phys. 36 2813-25
18. Nečas J 1967 Les méthodes directes en théorie des équations elliptiques (Paris: Masson et Cie, Editeurs)
19. Ruedenberg K and Scherr C W 1953 Free-electron network model for conjugated systems: I. Theory J. Chem. Phys. 21 1565-81
20. Reed M and Simon B 1972 Methods of Modern Mathematical Physics: Functional Analysis vol 1 (New York: Academic)
21. Reed M and Simon B 1978 Methods of Modern Mathematical Physics: Analysis of Operators vol 4 (New York: Academic)
22. Reed M and Simon B 1979 Methods of Modern Mathematical Physics: Scattering Theory vol 3 (New York: Academic)
23. Showalter R E 1977 Hilbert Space Methods for Partial Differential Equations (Monographs and Studies in Mathematics vol 1) (London: Pitman)