Curvature-induced resonances in a two-dimensional Dirichlet tube
Annales de l'I.H.P. Physique théorique, Volume 62 (1995) no. 1, pp. 81-101.
     author = {Duclos, P. and Exner, P. and \v{S}\v{t}ov{\'\i}\v{c}ek, P.},
     title = {Curvature-induced resonances in a two-dimensional {Dirichlet} tube},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {81--101},
     publisher = {Gauthier-Villars},
     volume = {62},
     number = {1},
     year = {1995},
     mrnumber = {1313362},
     zbl = {0838.35091},
     language = {en},
     url = {}
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AU  - Exner, P.
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%0 Journal Article
%A Duclos, P.
%A Exner, P.
%A Šťovíček, P.
%T Curvature-induced resonances in a two-dimensional Dirichlet tube
%J Annales de l'I.H.P. Physique théorique
%D 1995
%P 81-101
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%N 1
%I Gauthier-Villars
%G en
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Duclos, P.; Exner, P.; Šťovíček, P. Curvature-induced resonances in a two-dimensional Dirichlet tube. Annales de l'I.H.P. Physique théorique, Volume 62 (1995) no. 1, pp. 81-101.

[AC] J. Aguilar and J.-M. Combes, A class of analytic perturbation for one-body Schrödinger Hamiltonians, Commun. Math. Phys., Vol. 22, 1971, pp. 269-279. | MR | Zbl

[AD] J. Asch and P. Duclos, An elementary model of dynamical tunneling, in Proceedings of the Georgia Tech-UAB International Conference, "Differential equations with applications to mathematical physics"; W. F. Ames, E. M. Harrell II, J. V. Herod eds, Academic Press, New York, 1993, pp. 1-11. | MR | Zbl

[BD] V.S. Buslaev and L. Dmitrieva, A Bloch electron in an external field, Leningrad Math. J., Vol. 1, 1990, pp. 287-320. | MR | Zbl

[CE] H.L. Cycon and C. Erdmann, Absence of high energy resonances for many body Schrödinger operators, Rep. Math. Phys., Vol. 23, 1986, pp. 169-176. | MR | Zbl

[D] P. Duclos, On a global approach to the location of quantum resonances, in Proceedings of the Symposium on Partial Differential Equation and Mathematical Physics (M. Demuth, B. Schultze eds), Operator Theory: Advances and Applications, Vol. 57, Birkhäuser, Basel, 1992, pp. 39-49. | MR | Zbl

[DE1] P. Duclos and P. Exner, Curvature-induced bound states in quantum waveguides in two and three dimensions, to appear in Rev. Math. Phys. | MR | Zbl

[E] P. Exner, A model of resonance scattering on curved quantum wires, Ann. Physik, Vol. 47, 1990, pp. 123-138. | MR

[EŠ] P. Exner and P. ŠEBA, Bound states in curved quantum waveguides, J. Math. Phys., Vol. 30, 1989, pp. 2574-2580. | MR | Zbl

[GR] I.S. Gradshteyn and I.M. Ryzhik, Tables of Integrals, Sums, Series and Products, Nauka, Moscow, 1971.

[GMS] V. Grecchi, A. Maioli and A. Sacchetti, Wannier ladders and perturbation theory, J. Phys., Vol. A26, 1993, pp. L379-L384. | Zbl

[Hu} W. Hunziker, Distortion analyticity and molecular resonance curves, Ann. Inst. Henri Poincaré, Vol. 45, 1986, pp. 339-358. | Numdam | MR | Zbl

[JK] A. Joye and Ch.-Ed. Pfister, Exponentially small adiabatic invariant for the Schrödinger equation, Commun. Math. Phys., Vol. 140, 1991, pp. 15-41. | MR | Zbl

[JKP] A. Joye, H. Kunz and Ch.-Ed. Pfister, Exponential decay and geometric aspect of transition probabilities in the adiabatic limit, Ann. Phys., Vol. 208, 1991, pp. 299-332. | MR | Zbl

[JS] V. Jakšič and J. Segert, Exponential approach to the adiabatic limit and the Landau-Zener formula, Rev. Math. Phys. Vol. 4, 1992, pp. 529-574. | MR | Zbl

[KR] N. Kaidi and M. Rouleux, Forme normale pour un hamiltonien a deux niveaux près d'un point de branchement (limite semiclassique), C. R. Acad. Sci., Vol. 317, 1993, pp. 359-364. | MR | Zbl

[Ka] T. Kato, Perturbation Theory for Linear Operators, Springer, Heidelberg, 1966. | Zbl

[Kle] M. Klein, On the mathematical theory of predissociation, Ann. Phys., Vol. 178, 1987, pp. 48-73. | MR | Zbl

[LL] L.D. Landau and E.M. Lifshitz, Quantum Mechanics, Nauka, Moscow, 1974.

[MA1] A. Martinez, Estimations sur l'effet tunnel microlocal, Séminaire E.D.P. de l'École Polytechnique VIII, 1992; Estimates on complex interactions in phase space, Math. Nachr., Vol. 167, 1994, pp. 203-254. | Numdam | MR

[MA2] A. Martinez, Precise exponential in adiabatic theory, Journ. Math. Phys., Vol. 35, (8), 1994, pp. 3889-3913. | MR | Zbl

[MT] S. Matsutani and H. Tsuru, Reflectionless quantum wire, J. Phys. Soc. Japan, Vol. 60, 1991, pp. 3640-3644. | MR

[MW] K. Morgenröther and R. Werner, Resonances and standing waves, Math. Meth. in the Appl. Sci., Vol. 9, 1987, pp. 105-126. | MR | Zbl

[NE] G. Nenciu, Linear adiabatic theory and applications: exponential estimates, Commun. Math. Phys., Vol. 152, 1993, p. 479. | MR | Zbl

[RS] M. Reed and B. Simon, Methods of Modern Mathematical Physics, III. Scattering Theory. IV. Analysis of Operators, Academic Press, New York, 1978, 1979. | MR | Zbl

[Sch] M. Schechter, Operator methods in Quantum Mechanics, North-Holland Publ. Co, New York, 1981. | MR | Zbl

[Wed] R. Weder, Spectral and scattering theory in deformed optical waveguides, J. Reine Angew. Math., Vol. 390, 1988, pp. 279-288. | MR | Zbl

[Wei] J. Weidmann, Linear Operators in Hilbert Space, Springer, Heidelberg, 1980. | MR