메뉴 건너뛰기




Volumn 280, Issue 12, 2007, Pages 1376-1416

Intermediate Hamiltonian via Glazman's splitting and analytic perturbation for meromorphic matrix-functions

Author keywords

DN map; Quantum network; Scattering

Indexed keywords


EID: 34548553362     PISSN: 0025584X     EISSN: 15222616     Source Type: Journal    
DOI: 10.1002/mana.200610553     Document Type: Article
Times cited : (31)

References (90)
  • 1
    • 0001925902 scopus 로고
    • Quantum field-effect directional coupler
    • J. del Alamo and C. Eugster, Quantum field-effect directional coupler, Appl. Phys. Letters 56, No. 1, 78-83 (1990).
    • (1990) Appl. Phys. Letters , vol.56 , Issue.1 , pp. 78-83
    • del Alamo, J.1    Eugster, C.2
  • 2
    • 0003337424 scopus 로고
    • Scattering matrices for microschemes
    • V. Adamyan, Scattering matrices for microschemes, Oper. Theory Adv. Appl. 59, 1-10 (1992).
    • (1992) Oper. Theory Adv. Appl , vol.59 , pp. 1-10
    • Adamyan, V.1
  • 3
    • 0002969455 scopus 로고    scopus 로고
    • Spectral decomposition of selfadjoint block operator matrices with unbounded entries
    • V. Adamyan, H. Langer, and R. Mennicken, Spectral decomposition of selfadjoint block operator matrices with unbounded entries, Math. Nachr. 178, 43-80 (1996).
    • (1996) Math. Nachr , vol.178 , pp. 43-80
    • Adamyan, V.1    Langer, H.2    Mennicken, R.3
  • 4
    • 3042526641 scopus 로고    scopus 로고
    • M-operators: A generalization of Weyl-Titchmarsh Theory
    • W. O. Amrein and D. B. Pearson, M-operators: a generalization of Weyl-Titchmarsh Theory, J. Comput. Appl. Math. 171, No. 1-2, 1-26 (2004).
    • (2004) J. Comput. Appl. Math , vol.171 , Issue.1-2 , pp. 1-26
    • Amrein, W.O.1    Pearson, D.B.2
  • 5
    • 84990727688 scopus 로고
    • Generalized spectral decompositions of mixing dynamical systems
    • I. Antoniou and S. Tasaki, Generalized spectral decompositions of mixing dynamical systems, Int. J. Quantum Chem. 46, No. 3, 425-476 (1993).
    • (1993) Int. J. Quantum Chem , vol.46 , Issue.3 , pp. 425-476
    • Antoniou, I.1    Tasaki, S.2
  • 9
    • 37149037543 scopus 로고
    • Quantum transport in semiconductor nanostructures
    • edited by H. Ehrenreich and D. Turnbull Academic Press, San Diego
    • C. W. J. Beenakker and H. van Houten, Quantum transport in semiconductor nanostructures, in: Solid State Physics: Advances in Research and Applications Vol. 44, edited by H. Ehrenreich and D. Turnbull (Academic Press, San Diego, 1991), pp. 1-228.
    • (1991) Solid State Physics: Advances in Research and Applications , vol.44 , pp. 1-228
    • Beenakker, C.W.J.1    van Houten, H.2
  • 10
    • 34548585339 scopus 로고    scopus 로고
    • V. Bogevolnov, A. Mikhailova, B. Pavlov, and A. Yafyasov, About Scattering on the Ring, in: Israel Gohberg Anniversary edited by A. Dijksma, A. M. Kaashoek, and A. C. M. Ran, Operator Theory: Advances and Applications 124 (Birkhäuser, Basel, 2001), pp. 155-187.
    • V. Bogevolnov, A. Mikhailova, B. Pavlov, and A. Yafyasov, About Scattering on the Ring, in: Israel Gohberg Anniversary Volume, edited by A. Dijksma, A. M. Kaashoek, and A. C. M. Ran, Operator Theory: Advances and Applications Vol. 124 (Birkhäuser, Basel, 2001), pp. 155-187.
  • 11
    • 1642580772 scopus 로고    scopus 로고
    • Spectral inclusion and spectral exactness for PDEs on exterior domain
    • B. M. Brown and M. Marietta, Spectral inclusion and spectral exactness for PDEs on exterior domain, IMA J. Numer. Anal. 24, No. 1, 21-43 (2004).
    • (2004) IMA J. Numer. Anal , vol.24 , Issue.1 , pp. 21-43
    • Brown, B.M.1    Marietta, M.2
  • 13
    • 8744270531 scopus 로고
    • Generalized many-channel conductance formula with application to small rings
    • M. Büttiker, Y. Imry, R. Landauer, and S. Pinhas, Generalized many-channel conductance formula with application to small rings, Phys. Rev. B 31, 6207-6215 (1985).
    • (1985) Phys. Rev. B , vol.31 , pp. 6207-6215
    • Büttiker, M.1    Imry, Y.2    Landauer, R.3    Pinhas, S.4
  • 14
    • 4244144910 scopus 로고
    • Dynamic conductance and the scattering matrix of small conductors
    • M. Büttiker, A. Pretre, and H. Thomas, Dynamic conductance and the scattering matrix of small conductors, Phys. Rev. Lett. 70, 4114-4117 (1993).
    • (1993) Phys. Rev. Lett , vol.70 , pp. 4114-4117
    • Büttiker, M.1    Pretre, A.2    Thomas, H.3
  • 15
    • 3343011966 scopus 로고    scopus 로고
    • Adjoint and self-adjoint differential operators on graphs
    • R. Carlson, Adjoint and self-adjoint differential operators on graphs, Electron. J. Differential Equations 6, 1-10 (1998).
    • (1998) Electron. J. Differential Equations , vol.6 , pp. 1-10
    • Carlson, R.1
  • 16
    • 34548572239 scopus 로고    scopus 로고
    • X. Claeys, H. Haddar, and P. Jokly, Asymptotic models for diffraction by thin wires, in: Book of Abstracts of the AIMS Conference on Dynamical Systems, Differential Equations and Applications, Poitiers 25-28 June 2006 (Univ. of Poitiers, Poitiers, 2006), p. 66.
    • X. Claeys, H. Haddar, and P. Jokly, Asymptotic models for diffraction by thin wires, in: Book of Abstracts of the AIMS Conference on Dynamical Systems, Differential Equations and Applications, Poitiers 25-28 June 2006 (Univ. of Poitiers, Poitiers, 2006), p. 66.
  • 18
    • 34548590545 scopus 로고    scopus 로고
    • European Commission 1ST Programme: Future and Emerging Technologies
    • R. Compano (ed, 2nd edition Office for Official Publications of the European Communities, Luxemburg
    • R. Compano (ed.), European Commission 1ST Programme: Future and Emerging Technologies. Technology Roadmap for Nanoelectronics Vol. 105, 2nd edition (Office for Official Publications of the European Communities, Luxemburg, 2000).
    • (2000) Technology Roadmap for Nanoelectronics , vol.105
  • 20
    • 0001150826 scopus 로고
    • Eigenvalue estimates for certain noncompact manifolds
    • H. Donnely, Eigenvalue estimates for certain noncompact manifolds, Mich. Math. J. 31, 349-357 (1984).
    • (1984) Mich. Math. J , vol.31 , pp. 349-357
    • Donnely, H.1
  • 21
    • 0003655370 scopus 로고
    • Research Notes in Mathematics 65 Pitman, Advanced Publishing Program, Boston-Mass.-London
    • M. S. P. Eastham and H. Kalf, Schrödinger type operators with continuous spectra, Research Notes in Mathematics Vol. 65 (Pitman, Advanced Publishing Program, Boston-Mass.-London, 1982), p. 281.
    • (1982) Schrödinger type operators with continuous spectra , pp. 281
    • Eastham, M.S.P.1    Kalf, H.2
  • 22
    • 0011090883 scopus 로고    scopus 로고
    • Eigenfunction decay and eigenvalues accumulation for the Laplacian on asymptotically perturbed waveguides
    • J. Edward, Eigenfunction decay and eigenvalues accumulation for the Laplacian on asymptotically perturbed waveguides, J. London Math. Soc. (2) 59, 620-636 (1999).
    • (1999) J. London Math. Soc. (2) , vol.59 , pp. 620-636
    • Edward, J.1
  • 23
    • 0001039337 scopus 로고
    • A new type of quantum interference transistor
    • P. Exner and P. Ŝeba, A new type of quantum interference transistor, Phys. Lett. A 129, No. 8-9, 477 (1988).
    • (1988) Phys. Lett. A , vol.129 , Issue.8-9 , pp. 477
    • Exner, P.1    Ŝeba, P.2
  • 24
    • 16244421065 scopus 로고    scopus 로고
    • Convergence of graph-like thin manifolds
    • P. Exner and O. Post, Convergence of graph-like thin manifolds, J. Geom. Phys. 54, No. 1, 77-115 (2005).
    • (2005) J. Geom. Phys , vol.54 , Issue.1 , pp. 77-115
    • Exner, P.1    Post, O.2
  • 25
    • 17844369513 scopus 로고
    • On a model of Friedrichs in the theory of perturbations of the continuous spectrum
    • L. Faddeev, On a model of Friedrichs in the theory of perturbations of the continuous spectrum, Trudy Mat. Inst. Steklov. 73, 292-313 (1964).
    • (1964) Trudy Mat. Inst. Steklov , vol.73 , pp. 292-313
    • Faddeev, L.1
  • 26
    • 0004034109 scopus 로고
    • Zero-sets of operator-functions with a positive imaginary part
    • Linear and Complex Analysis Problems 199 Research Problems, edited by V. Havin, S. Hruschev, and N. Nikolskii
    • L. Faddeev and B. Pavlov, Zero-sets of operator-functions with a positive imaginary part, in: Linear and Complex Analysis Problems (199 Research Problems), edited by V. Havin, S. Hruschev, and N. Nikolskii, Lecture Notes in Mathematics Vol. 1043, 124 (1984).
    • (1984) Lecture Notes in Mathematics , vol.1043 , pp. 124
    • Faddeev, L.1    Pavlov, B.2
  • 27
    • 84980077260 scopus 로고
    • On perturbation of continuous spectra
    • K. O. Friedrichs, On perturbation of continuous spectra, Comm. Pure Appl. Math. 1, 361-406 (1948).
    • (1948) Comm. Pure Appl. Math , vol.1 , pp. 361-406
    • Friedrichs, K.O.1
  • 30
    • 34548598522 scopus 로고    scopus 로고
    • F. Gesztesy and B. Simon, Inverse spectral analysis with partial information on the potential. I. The case of an a.c. component in the spectrum, in: Papers honoring the 60th birthday of Klaus Hepp and of Walter Hunziker, Part II, HeIv. Phys. Acta 70, No. 1-2, 66-71 (1997).
    • F. Gesztesy and B. Simon, Inverse spectral analysis with partial information on the potential. I. The case of an a.c. component in the spectrum, in: Papers honoring the 60th birthday of Klaus Hepp and of Walter Hunziker, Part II, HeIv. Phys. Acta 70, No. 1-2, 66-71 (1997).
  • 31
    • 29144485504 scopus 로고    scopus 로고
    • Non-selfadjoint operators, infinite determinants and some applications
    • F. Gesztesy, Y. Latushkin, M. Mitrea, and M. Zinchenko, Non-selfadjoint operators, infinite determinants and some applications, Russ. J. Math. Phys. 12, 443-471 (2005).
    • (2005) Russ. J. Math. Phys , vol.12 , pp. 443-471
    • Gesztesy, F.1    Latushkin, Y.2    Mitrea, M.3    Zinchenko, M.4
  • 32
    • 34548580528 scopus 로고    scopus 로고
    • On Dirichlet-to-Neumann maps and some applications to modified Fredholm determinants
    • preprint
    • F. Gesztesy, M. Mitrea, and M. Zinchenko, On Dirichlet-to-Neumann maps and some applications to modified Fredholm determinants, preprint (2006).
    • (2006)
    • Gesztesy, F.1    Mitrea, M.2    Zinchenko, M.3
  • 33
    • 34548583466 scopus 로고    scopus 로고
    • I. 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).
    • I. 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).
  • 34
    • 0000201706 scopus 로고
    • Operator extension of the theorem about logarithmic residue and Rouché theorem
    • I. S. Gohberg and E. I. Sigal, Operator extension of the theorem about logarithmic residue and Rouché theorem, Mat. Sb. (N.S.) 84, 607-629 (1971).
    • (1971) Mat. Sb. (N.S.) , vol.84 , pp. 607-629
    • Gohberg, I.S.1    Sigal, E.I.2
  • 35
    • 33745830836 scopus 로고    scopus 로고
    • The first eigenvalue of the Laplacian isoperimetric constants and max flow min cut theorem
    • D. Grieser, The first eigenvalue of the Laplacian isoperimetric constants and max flow min cut theorem, Arch. Math. (Basel) 87, No. 1, 75-85 (2006).
    • (2006) Arch. Math. (Basel) , vol.87 , Issue.1 , pp. 75-85
    • Grieser, D.1
  • 36
    • 0000567144 scopus 로고
    • Théorie spectrale de qualques varietés àbouts, Ann. Sci. École Norm.Sp.
    • L. Guillopé, Théorie spectrale de qualques varietés àbouts, Ann. Sci. École Norm.Sp. (4) 22, No. 1, 137-160 (1989).
    • (1989) , vol.22 , Issue.1 , pp. 137-160
    • Guillopé, L.1
  • 37
    • 19144372654 scopus 로고    scopus 로고
    • Inverse scattering for the matrix Schrödinger operator and Schrödinger operator on graphs with general self-adjoint boundary conditions
    • M. Harmer, Inverse scattering for the matrix Schrödinger operator and Schrödinger operator on graphs with general self-adjoint boundary conditions, ANZIAM J. 43, No. 1, 161-168 (2002).
    • (2002) ANZIAM J , vol.43 , Issue.1 , pp. 161-168
    • Harmer, M.1
  • 38
    • 34548550621 scopus 로고    scopus 로고
    • G. Hellwig, Differential Operators of Mathematical Physics. An Introduction (Addison-Wesley Pub. Co. Reading, Mass.-London-Don Mills, Ont., 1967).
    • G. Hellwig, Differential Operators of Mathematical Physics. An Introduction (Addison-Wesley Pub. Co. Reading, Mass.-London-Don Mills, Ont., 1967).
  • 39
    • 84968483678 scopus 로고
    • Finite rank perturbations of singular spectra
    • J. Howland, Finite rank perturbations of singular spectra, Proc. Amer. Math. Soc. 97, No. 4, 634-636 (1986).
    • (1986) Proc. Amer. Math. Soc , vol.97 , Issue.4 , pp. 634-636
    • Howland, J.1
  • 40
    • 34548577207 scopus 로고    scopus 로고
    • V. O. Kalvine, P. Neittaanmäki, and B. A. Plamenevskii, Method for computing scattering matrices for general dissipative and self-adjoint elliptic problems in domain with cylindrical ends, J. Math. Sci., New York 122, No. 3, 3212-3245 (2004).
    • V. O. Kalvine, P. Neittaanmäki, and B. A. Plamenevskii, Method for computing scattering matrices for general dissipative and self-adjoint elliptic problems in domain with cylindrical ends, J. Math. Sci., New York 122, No. 3, 3212-3245 (2004).
  • 43
    • 0001747086 scopus 로고
    • Concerning the resolvents of an Hermitian operator with deficiency index (m, m)
    • M. Krein, Concerning the resolvents of an Hermitian operator with deficiency index (m, m), Dokl. Akad. Nauk USSR 52, 651 (1946).
    • (1946) Dokl. Akad. Nauk USSR , vol.52 , pp. 651
    • Krein, M.1
  • 44
    • 23444439127 scopus 로고    scopus 로고
    • On the spectrum of curved quantum waveguides
    • D. Krejcirik and J. Kriz, On the spectrum of curved quantum waveguides, Publ. Res. Inst. Math. Sci. 3, 757-791 (2005).
    • (2005) Publ. Res. Inst. Math. Sci , vol.3 , pp. 757-791
    • Krejcirik, D.1    Kriz, J.2
  • 45
    • 18744432050 scopus 로고    scopus 로고
    • The nature of the essential spectrum in curved quantum waveguides
    • D. Krejcirik and R. T. de Aldecoa, The nature of the essential spectrum in curved quantum waveguides, J. Phys. A, Math. Gen. 37, No. 20, 5449-5466 (2004).
    • (2004) J. Phys. A, Math. Gen , vol.37 , Issue.20 , pp. 5449-5466
    • Krejcirik, D.1    de Aldecoa, R.T.2
  • 46
    • 0035877564 scopus 로고    scopus 로고
    • Convergence of spectra of mesoscopic systems collapsing onto graph
    • P. Kuchment and H. Zeng, Convergence of spectra of mesoscopic systems collapsing onto graph, J. Math. Anal. Appl. 258, 671-700 (2001).
    • (2001) J. Math. Anal. Appl , vol.258 , pp. 671-700
    • Kuchment, P.1    Zeng, H.2
  • 47
    • 0036804366 scopus 로고    scopus 로고
    • Graph models for waves in thin structures
    • P. Kuchment, Graph models for waves in thin structures, Waves Random Media 12, No. 4, 1-24 (2002).
    • (2002) Waves Random Media , vol.12 , Issue.4 , pp. 1-24
    • Kuchment, P.1
  • 49
    • 0141865706 scopus 로고    scopus 로고
    • Structure-preserving model reduction for mechanical systems
    • S. Lall, P. Krysl, and J. Marsden, Structure-preserving model reduction for mechanical systems, Physica D 184, No. 1-4, 304-318 (2003).
    • (2003) Physica D , vol.184 , Issue.1-4 , pp. 304-318
    • Lall, S.1    Krysl, P.2    Marsden, J.3
  • 50
    • 84996237073 scopus 로고
    • Electrical resistance of disordered one-dimensional lattices
    • R. Landauer, Electrical resistance of disordered one-dimensional lattices, Phil. Mag. 21, 863 (1970).
    • (1970) Phil. Mag , vol.21 , pp. 863
    • Landauer, R.1
  • 52
    • 34548573066 scopus 로고    scopus 로고
    • M. Levitin, A simple calculation of eigenvalues and resonances in domains with regular ends, arXiv:math.SP/0611237, vl, 8 November 2006.
    • M. Levitin, A simple calculation of eigenvalues and resonances in domains with regular ends, arXiv:math.SP/0611237, vl, 8 November 2006.
  • 53
    • 0005761101 scopus 로고
    • Introduction to Solid-state Theory
    • Springer-Verlag, Berlin-New York
    • O. Madelung, Introduction to Solid-state Theory, Springer Series in Solid-state Sciences Vol. 2 (Springer-Verlag, Berlin-New York, 1978).
    • (1978) Springer Series in Solid-state Sciences , vol.2
    • Madelung, O.1
  • 54
    • 3042626305 scopus 로고    scopus 로고
    • Eigenvalue problems on exterior domains and Dirichlet-to-Neumann map
    • M. Marletta, Eigenvalue problems on exterior domains and Dirichlet-to-Neumann map, J. Comput. Appl. Math. 171, No. 1-2, 367-392 (2004).
    • (2004) J. Comput. Appl. Math , vol.171 , Issue.1-2 , pp. 367-392
    • Marletta, M.1
  • 56
    • 21844487438 scopus 로고
    • Two-body scattering on a graph and application to simple nanoelectronic devices
    • Y Melnikov and B. Pavlov, Two-body scattering on a graph and application to simple nanoelectronic devices, J. Math. Phys. 366, 2813-2825 (1995).
    • (1995) J. Math. Phys , vol.366 , pp. 2813-2825
    • Melnikov, Y.1    Pavlov, B.2
  • 57
    • 0000822305 scopus 로고    scopus 로고
    • Spectral decomposition of symmetric operator matrices
    • R. Mennicken and A. Shkalikov, Spectral decomposition of symmetric operator matrices, Math. Nachr. 179, 259-273 (1996).
    • (1996) Math. Nachr , vol.179 , pp. 259-273
    • Mennicken, R.1    Shkalikov, A.2
  • 58
    • 34548587245 scopus 로고    scopus 로고
    • A. Mikhailova and B. Pavlov, Resonance quantum switch, in: Proceedings of the S. Kovalevski Symposium on Operator Methods in Ordinary and Partial Differential Equations, Univ. of Stockholm, June 2000, edited by S. Albeverio, N. Elander, W. N. Everitt, and P. Kurasov, Operator Methods: Advances and Applications 132 (Birkhäuser, BaselBoston-Berlin, 2002), pp. 287-322.
    • A. Mikhailova and B. Pavlov, Resonance quantum switch, in: Proceedings of the S. Kovalevski Symposium on Operator Methods in Ordinary and Partial Differential Equations, Univ. of Stockholm, June 2000, edited by S. Albeverio, N. Elander, W. N. Everitt, and P. Kurasov, Operator Methods: Advances and Applications Vol. 132 (Birkhäuser, BaselBoston-Berlin, 2002), pp. 287-322.
  • 59
    • 0005670503 scopus 로고    scopus 로고
    • Quantum domain as a triadic relay
    • edited by I. Antoniou, C. Calude, and M. J. Dinneeen, Springer-Verlag Series for Discrete Mathematics and Theoretical Computer Science Springer-Verlag
    • A. Mikhailova and B. Pavlov, Quantum domain as a triadic relay, in: Unconventional Models of Computations UMC ' 2K, edited by I. Antoniou, C. Calude, and M. J. Dinneeen, Springer-Verlag Series for Discrete Mathematics and Theoretical Computer Science (Springer-Verlag, 2001), pp. 167-186.
    • (2001) Unconventional Models of Computations UMC ' 2K , pp. 167-186
    • Mikhailova, A.1    Pavlov, B.2
  • 60
    • 34247856487 scopus 로고    scopus 로고
    • Modelling of quantum networks
    • arXiv math-ph/031238
    • A. Mikhailova, B. Pavlov, and L. Prokhorov, Modelling of quantum networks, arXiv math-ph/031238 (2004).
    • (2004)
    • Mikhailova, A.1    Pavlov, B.2    Prokhorov, L.3
  • 61
    • 34548548697 scopus 로고    scopus 로고
    • R. Mittra and S. Lee, Analytical Techniques in the Theory of Guided Waves (The Macmillan Company, NY; CollierMacmillan Limited, London, 1971).
    • R. Mittra and S. Lee, Analytical Techniques in the Theory of Guided Waves (The Macmillan Company, NY; CollierMacmillan Limited, London, 1971).
  • 63
    • 34548591500 scopus 로고    scopus 로고
    • S. N. Naboko, Non-tangential boundary values of operator-valued R-functions in a half plane, Leningrad Math. Journal 1, No. 5, 1255-1277 (1990).
    • S. N. Naboko, Non-tangential boundary values of operator-valued R-functions in a half plane, Leningrad Math. Journal 1, No. 5, 1255-1277 (1990).
  • 64
    • 1942501049 scopus 로고    scopus 로고
    • Analysis of the dispersion equation for die Schrödinger equation on periodic metric graphs
    • V. I. Oleinik, B. S. Pavlov, and N. V. Sibirev, Analysis of the dispersion equation for die Schrödinger equation on periodic metric graphs, Waves Random Media 14, 157-183 (2004).
    • (2004) Waves Random Media , vol.14 , pp. 157-183
    • Oleinik, V.I.1    Pavlov, B.S.2    Sibirev, N.V.3
  • 65
    • 21844497792 scopus 로고
    • Spectral asymptotics of the Laplace operator on manifolds with cylindrical ends
    • L. Parnovski, Spectral asymptotics of the Laplace operator on manifolds with cylindrical ends, Internat. J. Math. 6, No. 6, 911-920 (1995).
    • (1995) Internat. J. Math , vol.6 , Issue.6 , pp. 911-920
    • Parnovski, L.1
  • 66
    • 34548561869 scopus 로고    scopus 로고
    • B. Pavlov, S-matrix and Dirichlet-to-Neumann Operators, in: Encyclopedia of Scattering, edited by R. Pike and P. Sabatier (Academic Press, Harcourt Science and Tech. Company, 2001).
    • B. Pavlov, S-matrix and Dirichlet-to-Neumann Operators, in: Encyclopedia of Scattering, edited by R. Pike and P. Sabatier (Academic Press, Harcourt Science and Tech. Company, 2001).
  • 67
    • 0001251353 scopus 로고    scopus 로고
    • B. Pavlov, On one-dimensional scattering of plane waves on an arbitrary potential, Teoret. Mat. Fiz. 16, No. 1, 105-119 (1973) (in Russian).
    • B. Pavlov, On one-dimensional scattering of plane waves on an arbitrary potential, Teoret. Mat. Fiz. 16, No. 1, 105-119 (1973) (in Russian).
  • 68
    • 19944367295 scopus 로고    scopus 로고
    • Jump-start in analytic perturbation procedure for Friedrichs model
    • B. Pavlov and I. Antoniou, Jump-start in analytic perturbation procedure for Friedrichs model, J. Phys. A, Math. Gen. 38, 4811-4823(2005).
    • (2005) J. Phys. A, Math. Gen , vol.38 , pp. 4811-4823
    • Pavlov, B.1    Antoniou, I.2
  • 69
    • 34247885914 scopus 로고    scopus 로고
    • A star-graph model via operator extension, Math
    • Soc, to appear
    • B. Pavlov, A star-graph model via operator extension, Math. Proc. Camb. Philos. Soc. 142, to appear.
    • Proc. Camb. Philos , vol.142
    • Pavlov, B.1
  • 71
    • 34250474446 scopus 로고
    • The singular spectrum of a weakly perturbed multiplication operator, Funktsional
    • in Russian
    • B. Pavlov and S. Petras, The singular spectrum of a weakly perturbed multiplication operator, Funktsional. Anal, i Prilozhen. 4, No. 2, 54-61 (1970) (in Russian).
    • (1970) Anal, i Prilozhen , vol.4 , Issue.2 , pp. 54-61
    • Pavlov, B.1    Petras, S.2
  • 73
    • 34548564038 scopus 로고
    • New Methods of Celestial Mechanics
    • Approximation by, American Institute of Physics, Inc, New York
    • H. Poincaré, New Methods of Celestial Mechanics Vol. 2: Approximation by Series (American Institute of Physics, Inc., New York, 1993).
    • (1993) Series , vol.2
    • Poincaré, H.1
  • 74
    • 0002147052 scopus 로고
    • A unified formulation of dynamics and thermodynamics
    • I. Prigogine, C. George, and L. Rosenfeld, A unified formulation of dynamics and thermodynamics, Chemica Scripta 4, No. 5 (1973).
    • (1973) Chemica Scripta , vol.4 , Issue.5
    • Prigogine, I.1    George, C.2    Rosenfeld, L.3
  • 75
    • 19944372818 scopus 로고    scopus 로고
    • I. Prigogine, Irreversibility as a symmetry-breaking process, Natur. J. 246, No. 9 (1973).
    • I. Prigogine, Irreversibility as a symmetry-breaking process, Natur. J. 246, No. 9 (1973).
  • 77
    • 84987159575 scopus 로고
    • Why irreversibility? The formulation of classical and quantum mechanics for nonintegrable systems
    • I. Prigogine, Why irreversibility? The formulation of classical and quantum mechanics for nonintegrable systems, Int. J. Quantum Chem. 53, 105 (1995).
    • (1995) Int. J. Quantum Chem , vol.53 , pp. 105
    • Prigogine, I.1
  • 79
    • 33746100468 scopus 로고
    • Das Eigenvertproblem von △u + λu = 0 in Halbrohren
    • January 8, Interscience Publishers, Inc, New York
    • F. Rellich, Das Eigenvertproblem von △u + λu = 0 in Halbrohren, in: Studies and Essays presented to R. Courant on the occasion of his 60th birthday, January 8, 1948 (Interscience Publishers, Inc., New York, 1948), pp. 329-344.
    • (1948) Studies and Essays presented to R. Courant on the occasion of his 60th birthday , pp. 329-344
    • Rellich, F.1
  • 80
    • 84975712426 scopus 로고    scopus 로고
    • On the eigenvalues of the Laplace operator on a thin set with Neumann boundary conditions
    • M. Schatzman, On the eigenvalues of the Laplace operator on a thin set with Neumann boundary conditions, Appl. Anal. 61, No. 3-4, 243-306 (1996).
    • (1996) Appl. Anal , vol.61 , Issue.3-4 , pp. 243-306
    • Schatzman, M.1
  • 83
    • 0036019318 scopus 로고    scopus 로고
    • Schrödinger operators on homogeneous metric trees: Spectrum in gaps
    • A. Sobolev and M. Solomyak, Schrödinger operators on homogeneous metric trees: spectrum in gaps, Rev. Math. Phys. 14, No. 5, 421-467 (2002).
    • (2002) Rev. Math. Phys , vol.14 , Issue.5 , pp. 421-467
    • Sobolev, A.1    Solomyak, M.2
  • 84
    • 0942278569 scopus 로고    scopus 로고
    • On the spectrum of Laplacian on regular metric trees
    • M. Z. Solomyak, On the spectrum of Laplacian on regular metric trees, Waves Random Media 14, No. 1, 155 (2004).
    • (2004) Waves Random Media , vol.14 , Issue.1 , pp. 155
    • Solomyak, M.Z.1
  • 87
    • 0008597896 scopus 로고
    • Reaction-diffusion equations with randomly perturbed boundary conditions
    • A. Wentzel and M. Freidlin, Reaction-diffusion equations with randomly perturbed boundary conditions, Ann. Probab. 20, No. 2, 963-986 (1992).
    • (1992) Ann. Probab , vol.20 , Issue.2 , pp. 963-986
    • Wentzel, A.1    Freidlin, M.2
  • 88
    • 0035794337 scopus 로고    scopus 로고
    • Electrical properties of three-terminal ballistic junction
    • H. Q. Xu, Electrical properties of three-terminal ballistic junction, Applied Phys. Letters 78, 2064 (2001).
    • (2001) Applied Phys. Letters , vol.78 , pp. 2064
    • Xu, H.Q.1
  • 89
    • 79956021220 scopus 로고    scopus 로고
    • Diode and transistor behaviour of three-terminal ballistic junctions
    • H. Q. Xu, Diode and transistor behaviour of three-terminal ballistic junctions, Applied Phys. Letters 80, 853 (2002).
    • (2002) Applied Phys. Letters , vol.80 , pp. 853
    • Xu, H.Q.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.