메뉴 건너뛰기




Volumn 38, Issue 22, 2005, Pages 4887-4900

Quantum graphs: II. Some spectral properties of quantum and combinatorial graphs

Author keywords

[No Author keywords available]

Indexed keywords


EID: 19944375123     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/38/22/013     Document Type: Article
Times cited : (227)

References (45)
  • 2
    • 12044260159 scopus 로고
    • Periodic Schrï¿1/2dinger operators with large gaps and Wannier-Stark ladders
    • 10.1103/PhysRevLett.72.896 0031-9007
    • Avron J, Exner P and Last Y 1994 Periodic Schrï¿1/2dinger operators with large gaps and Wannier-Stark ladders Phys. Rev. Lett. 72 869-99
    • (1994) Phys. Rev. Lett. , vol.72 , Issue.6 , pp. 896-899
    • Avron, J.1    Exner, P.2    Last, Y.3
  • 3
    • 0001890867 scopus 로고    scopus 로고
    • A periodic magnetic Hamiltonian with a variable metric. The problem of absolute continuity
    • 0234-0852
    • Sh Birman M and Suslina T A 2000 A periodic magnetic Hamiltonian with a variable metric. The problem of absolute continuity Algebra i Analiz 11 no. 2 pp 1-40
    • (2000) Algebra I Analiz , vol.11 , pp. 21-40
    • Birman, Sh.M.1    Suslina, T.A.2
  • 10
    • 0000274654 scopus 로고
    • Lattice Kronig-Penney models
    • 10.1103/PhysRevLett.74.3503 0031-9007
    • Exner P 1995 Lattice Kronig-Penney models Phys. Rev. Lett. 74 3503-6
    • (1995) Phys. Rev. Lett. , vol.74 , Issue.18 , pp. 3503-3506
    • Exner, P.1
  • 11
    • 0002950593 scopus 로고
    • Electrons in semiconductor microstructures: A challenge to operator theorists
    • Exner P and Šeba P 1989 Electrons in semiconductor microstructures: a challenge to operator theorists Schrödinger Operators, Standard and Nonstandard (Dubna 1988) (Singapore: World Scientific) pp 79-100
    • (1989) Schrödinger Operators, Standard and Nonstandard , pp. 79-100
    • Exner, P.1    Šeba, P.2
  • 12
    • 0001957495 scopus 로고
    • Free quantum motion on a branching graph
    • 10.1016/0034-4877(89)90023-2 0034-4877
    • Exner P and Šeba P 1989 Free quantum motion on a branching graph Rep. Math. Phys. 28 7-26
    • (1989) Rep. Math. Phys. , vol.28 , Issue.1 , pp. 7-26
    • Exner, P.1    Šeba, P.2
  • 13
    • 0032048516 scopus 로고    scopus 로고
    • Spectral properties of classical waves in high contrast periodic media
    • 10.1137/S0036139996297249 0036-1399
    • Figotin A and Kuchment P 1998 Spectral properties of classical waves in high contrast periodic media SIAM J. Appl. Math. 58 683-702
    • (1998) SIAM J. Appl. Math. , vol.58 , Issue.2 , pp. 683-702
    • Figotin, A.1    Kuchment, P.2
  • 14
    • 0011412457 scopus 로고
    • On the spectrum of a class of second order periodic elliptic differential operators
    • Friedlander L 1990 On the spectrum of a class of second order periodic elliptic differential operators Commun. Partial Differ. Eq. 15 1631-47
    • (1990) Commun. Partial Differ. Eq. , vol.15 , pp. 1631-1647
    • Friedlander, L.1
  • 15
    • 17644437865 scopus 로고    scopus 로고
    • The Mourre theory for analytically fibered operators
    • 10.1006/jfan.1997.3154 0022-1236
    • Gerard C and Nier F 1998 The Mourre theory for analytically fibered operators J. Funct. Anal. 152 202-19
    • (1998) J. Funct. Anal. , vol.152 , Issue.1 , pp. 202-219
    • Gerard, C.1    Nier, F.2
  • 17
    • 0034704432 scopus 로고    scopus 로고
    • Hermitian symplectic geometry and extension theory
    • 0305-4470 305
    • Harmer M 2000 Hermitian symplectic geometry and extension theory J. Phys. A: Math. Gen. 33 9193-203
    • (2000) J. Phys. A: Math. Gen. , vol.33 , Issue.50 , pp. 9193-9203
    • Harmer, M.1
  • 20
    • 0033613617 scopus 로고    scopus 로고
    • Kirchhoff's rule for quantum wires
    • 0305-4470 006
    • Kostrykin V and Schrader R 1999 Kirchhoff's rule for quantum wires J. Phys. A: Math. Gen. 32 595-630
    • (1999) J. Phys. A: Math. Gen. , vol.32 , Issue.4 , pp. 595-630
    • Kostrykin, V.1    Schrader, R.2
  • 21
    • 0001257553 scopus 로고    scopus 로고
    • Quantum chaos on graphs
    • 10.1103/PhysRevLett.79.4794 0031-9007
    • Kottos T and Smilansky U 1997 Quantum chaos on graphs Phys. Rev. Lett. 79 4794-97
    • (1997) Phys. Rev. Lett. , vol.79 , Issue.24 , pp. 4794-4797
    • Kottos, T.1    Smilansky, U.2
  • 24
    • 0001325714 scopus 로고    scopus 로고
    • The mathematics of photonics crystals
    • Kuchment P 2001 The mathematics of photonics crystals Mathematical Modeling in Optical Science ed G Bao, L Cowsar and W Masters (Philadelphia, PA: SIAM) pp 207-72
    • (2001) Mathematical Modeling in Optical Science , pp. 207-272
    • Kuchment, P.1
  • 25
    • 0942280564 scopus 로고    scopus 로고
    • Differential and pseudo-differential operators on graphs as models of mesoscopic systems
    • Kuchment P 2003 Differential and pseudo-differential operators on graphs as models of mesoscopic systems Analysis and Applications ed H Begehr, R Gilbert and M W Wang (Dordrecht: Kluwer) pp 7-30
    • (2003) Analysis and Applications , pp. 7-30
    • Kuchment, P.1
  • 26
    • 0036804366 scopus 로고    scopus 로고
    • Graph models of wave propagation in thin structures
    • 10.1088/0959-7174/12/4/201 0959-7174
    • Kuchment P 2002 Graph models of wave propagation in thin structures Waves Random Media 12 R1-R24
    • (2002) Waves Random Media , vol.12 , Issue.4
    • Kuchment, P.1
  • 27
    • 0942278598 scopus 로고    scopus 로고
    • Quantum graphs: I. Some basic structures
    • 10.1088/0959-7174/14/1/014 0959-7174
    • Kuchment P 2004 Quantum graphs: I. Some basic structures Waves Random Media 14 S107-S128
    • (2004) Waves Random Media , vol.14 , Issue.1
    • Kuchment, P.1
  • 28
    • 19944363603 scopus 로고    scopus 로고
    • On some spectral problems of mathematical physics
    • Kuchment P 2004 On some spectral problems of mathematical physics Partial Differential Equations and Inverse Problems (Contemp. Math. vol 362) ed C Conca, R Manasevich, G Uhlmann and M S Vogelius (Providence, RI: American Mathematical Society) pp 241-76
    • (2004) Partial Differential Equations and Inverse Problems , pp. 241-276
    • Kuchment, P.1
  • 29
    • 0033245667 scopus 로고    scopus 로고
    • Spectral properties of high contrast band-gap materials and operators on graphs
    • Kuchment P and Kunyansky L 1999 Spectral properties of high contrast band-gap materials and operators on graphs Exp. Math. 8 1-28
    • (1999) Exp. Math. , vol.8 , pp. 1-28
    • Kuchment, P.1    Kunyansky, L.2
  • 30
    • 0036109923 scopus 로고    scopus 로고
    • Differential operators on graphs and photonic crystals
    • 10.1023/A:1014481629504 1019-7168
    • Kuchment P and Kunyansky L 2002 Differential operators on graphs and photonic crystals Adv. Comput. Math. 16 263-90
    • (2002) Adv. Comput. Math. , vol.16 , pp. 263-290
    • Kuchment, P.1    Kunyansky, L.2
  • 31
    • 0036035440 scopus 로고    scopus 로고
    • On the structure of spectra of periodic elliptic operators
    • 10.1090/S0002-9947-01-02878-1 0002-9947
    • Kuchment P and Levendorskii S 2002 On the structure of spectra of periodic elliptic operators Trans. AMS 354 537-69
    • (2002) Trans. AMS , vol.354 , Issue.2 , pp. 537-569
    • Kuchment, P.1    Levendorskii, S.2
  • 32
    • 19944388994 scopus 로고
    • Lang S 1985 (New York: Springer)
    • (1985)
    • Lang, S.1
  • 33
    • 0039646395 scopus 로고    scopus 로고
    • Schrödinger operators on graphs and topology
    • Novikov S 1997 Schrödinger operators on graphs and topology Russ. Math. Surv. 52 177-8
    • (1997) Russ. Math. Surv. , vol.52 , pp. 177-178
    • Novikov, S.1
  • 34
    • 0001533137 scopus 로고    scopus 로고
    • Discrete Schrödinger operators and topology
    • Novikov S 1999 Discrete Schrödinger operators and topology Asian Math. J. 2 841-53
    • (1999) Asian Math. J. , vol.2 , pp. 841-853
    • Novikov, S.1
  • 36
    • 0040690706 scopus 로고
    • A model of zero-radius potential with internal structure
    • 10.1007/BF01018192 0040-5779
    • Pavlov B S 1984 A model of zero-radius potential with internal structure Theor. Math. Phys. 59 544-80
    • (1984) Theor. Math. Phys. , vol.59 , Issue.3 , pp. 544-580
    • Pavlov, B.S.1
  • 37
    • 76549105667 scopus 로고
    • The theory of extensions and explicitly solvable models
    • 0036-0279
    • Pavlov B S 1987 The theory of extensions and explicitly solvable models Russ. Math. Surv. 42 127-68
    • (1987) Russ. Math. Surv. , vol.42 , pp. 127-168
    • Pavlov, B.S.1
  • 38
    • 19944378533 scopus 로고    scopus 로고
    • Quantum graphs and their applications
    • Kuchment P (ed) 2004 Quantum graphs and their applications Waves Random Media 14 (1) S1-185
    • (2004) Waves Random Media , vol.141 , pp. 1-185
    • Kuchment, P.1
  • 40
    • 0011159603 scopus 로고    scopus 로고
    • The creation of spectral gaps by graph decoration
    • 10.1023/A:1011032212489 0377-9017
    • Schenker J and Aizenman M 2000 The creation of spectral gaps by graph decoration Lett. Math. Phys. 53 253
    • (2000) Lett. Math. Phys. , vol.53 , Issue.3 , pp. 253
    • Schenker, J.1    Aizenman, M.2
  • 41
    • 0000695627 scopus 로고
    • On the behavior of eigenfunctions of the Schrödinger equation
    • Schnol E 1957 On the behavior of eigenfunctions of the Schrödinger equation Mat. Sbornik 42 273-86
    • (1957) Mat. Sbornik , vol.42 , pp. 273-286
    • Schnol, E.1
  • 42
    • 0001823985 scopus 로고
    • Spectral theory of elliptic operators on non-compact manifolds, methodes semi-classiques, vol I (Nantes, 1990)
    • 0303-1179
    • Shubin M A 1992 Spectral theory of elliptic operators on non-compact manifolds, methodes semi-classiques, vol I (Nantes, 1990) Asterisque 207 35-108
    • (1992) Asterisque , vol.207 , pp. 35-108
    • Shubin, M.A.1
  • 43
    • 4243435891 scopus 로고    scopus 로고
    • Spectral theory of elliptic operators on non-compact manifolds: Qualitative results
    • Shubin M A 1999 Spectral theory of elliptic operators on non-compact manifolds: qualitative results Spectral Theory and Geometry (Edinburgh, 1998) (London Math. Soc. Lect. Ser. vol 273) (Cambridge: Cambridge University Press) pp 226-83
    • (1999) Spectral Theory and Geometry , pp. 226-283
    • Shubin, M.A.1
  • 44
    • 0942278569 scopus 로고    scopus 로고
    • On the spectrum of the Laplacian on regular metric trees
    • 10.1088/0959-7174/14/1/017 0959-7174
    • Solomyak M 2004 On the spectrum of the Laplacian on regular metric trees Waves Random Media 14 S155-S171
    • (2004) Waves Random Media , vol.14 , Issue.1
    • Solomyak, M.1
  • 45
    • 0000485145 scopus 로고
    • Time dependent approach to scattering from impurities in a crystal
    • 10.1007/BF01646745 0010-3616
    • Thomas L E 1973 Time dependent approach to scattering from impurities in a crystal Commun. Math. Phys. 33 335-43
    • (1973) Commun. Math. Phys. , vol.33 , Issue.4 , pp. 335-343
    • Thomas, L.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.