@article{AIHPA_1995__62_1_81_0, author = {Duclos, Pierre and Exner, P. and \v S\v tov\'\i \v cek, P.}, title = {Curvature-induced resonances in a two-dimensional Dirichlet tube}, journal = {Annales de l'I.H.P. Physique th\'eorique}, volume = {63}, year = {1995}, pages = {81-101}, mrnumber = {1313362}, zbl = {0838.35091}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPA_1995__62_1_81_0} }
Duclos, P.; Exner, P.; Šťovíček, P. Curvature-induced resonances in a two-dimensional Dirichlet tube. Annales de l'I.H.P. Physique théorique, Tome 63 (1995) pp. 81-101. http://gdmltest.u-ga.fr/item/AIHPA_1995__62_1_81_0/
[AC] A class of analytic perturbation for one-body Schrödinger Hamiltonians, Commun. Math. Phys., Vol. 22, 1971, pp. 269-279. | MR 345551 | Zbl 0219.47011
and ,[AD] 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 1207143 | Zbl 0789.35127
and ,[BD] A Bloch electron in an external field, Leningrad Math. J., Vol. 1, 1990, pp. 287-320. | MR 1025153 | Zbl 0726.34070
and ,[CE] Absence of high energy resonances for many body Schrödinger operators, Rep. Math. Phys., Vol. 23, 1986, pp. 169-176. | MR 894910 | Zbl 0646.35017
and ,[D] 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 1230889 | Zbl 0877.47038
,[DE1] Curvature-induced bound states in quantum waveguides in two and three dimensions, to appear in Rev. Math. Phys. | MR 1310767 | Zbl 0837.35037
and ,[E] A model of resonance scattering on curved quantum wires, Ann. Physik, Vol. 47, 1990, pp. 123-138. | MR 1066095
,[EŠ] P. ŠEBA, Bound states in curved quantum waveguides, J. Math. Phys., Vol. 30, 1989, pp. 2574-2580. | MR 1019002 | Zbl 0693.46066
and[GR] Tables of Integrals, Sums, Series and Products, Nauka, Moscow, 1971.
and ,[GMS] Wannier ladders and perturbation theory, J. Phys., Vol. A26, 1993, pp. L379-L384. | Zbl 0772.34059
, and ,[Hu} Distortion analyticity and molecular resonance curves, Ann. Inst. Henri Poincaré, Vol. 45, 1986, pp. 339-358. | Numdam | MR 880742 | Zbl 0619.46068
,[JK] Exponentially small adiabatic invariant for the Schrödinger equation, Commun. Math. Phys., Vol. 140, 1991, pp. 15-41. | MR 1124257 | Zbl 0755.35104
and ,[JKP] Exponential decay and geometric aspect of transition probabilities in the adiabatic limit, Ann. Phys., Vol. 208, 1991, pp. 299-332. | MR 1110431 | Zbl 0875.60022
, and ,[JS] Exponential approach to the adiabatic limit and the Landau-Zener formula, Rev. Math. Phys. Vol. 4, 1992, pp. 529-574. | MR 1197550 | Zbl 0769.34006
and ,[KR] 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 1235449 | Zbl 0797.58083
and ,[Ka] Perturbation Theory for Linear Operators, Springer, Heidelberg, 1966. | Zbl 0148.12601
,[Kle] On the mathematical theory of predissociation, Ann. Phys., Vol. 178, 1987, pp. 48-73. | MR 913151 | Zbl 0649.35024
,[LL] Quantum Mechanics, Nauka, Moscow, 1974.
and ,[MA1] 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 1226487
,[MA2] Precise exponential in adiabatic theory, Journ. Math. Phys., Vol. 35, (8), 1994, pp. 3889-3913. | MR 1284618 | Zbl 0808.47053
,[MT] Reflectionless quantum wire, J. Phys. Soc. Japan, Vol. 60, 1991, pp. 3640-3644. | MR 1152471
and ,[MW] Resonances and standing waves, Math. Meth. in the Appl. Sci., Vol. 9, 1987, pp. 105-126. | MR 881556 | Zbl 0639.35045
and ,[NE] Linear adiabatic theory and applications: exponential estimates, Commun. Math. Phys., Vol. 152, 1993, p. 479. | MR 1213299 | Zbl 0768.34038
,[RS] Methods of Modern Mathematical Physics, III. Scattering Theory. IV. Analysis of Operators, Academic Press, New York, 1978, 1979. | MR 529429 | Zbl 0405.47007
and ,[Sch] Operator methods in Quantum Mechanics, North-Holland Publ. Co, New York, 1981. | MR 597895 | Zbl 0456.47012
,[Wed] Spectral and scattering theory in deformed optical waveguides, J. Reine Angew. Math., Vol. 390, 1988, pp. 279-288. | MR 953682 | Zbl 0644.35080
,[Wei] Linear Operators in Hilbert Space, Springer, Heidelberg, 1980. | MR 566954
,