Absence of geometrical phases in the rotating stark effect
Caliceti, Emanuela ; Marmi, Stefano ; Nardini, Franco
Annales de l'I.H.P. Physique théorique, Tome 56 (1992), p. 279-305 / Harvested from Numdam
Publié le : 1992-01-01
@article{AIHPA_1992__56_3_279_0,
     author = {Caliceti, Emanuela and Marmi, Stefano and Nardini, Franco},
     title = {Absence of geometrical phases in the rotating stark effect},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {56},
     year = {1992},
     pages = {279-305},
     mrnumber = {1160852},
     zbl = {0757.35064},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1992__56_3_279_0}
}
Caliceti, Emanuela; Marmi, Stefano; Nardini, Franco. Absence of geometrical phases in the rotating stark effect. Annales de l'I.H.P. Physique théorique, Tome 56 (1992) pp. 279-305. http://gdmltest.u-ga.fr/item/AIHPA_1992__56_3_279_0/

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 345551 | Zbl 0219.47011

Y. Aharonov and J. Anandan, Phase Change During a Cyclic Quantum Evolution, Phys. Rev. Lett., Vol. 58, 1987, pp. 1593-1596. | MR 884314

V.I. Arnol'D, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer-Verlag, New York, Heidelberg, Berlin, 1983. | MR 695786

V.I. Arnol'D, V.V. Kozlov and A.I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics, Encyclopaedia of Mathematical Sciences, Vol. 3, Dynamical Systems, III Springer-Verlag, Berlin, 1988. | MR 1292465

G. Auberson and G. Mennessier, Some Properties of Borel Summable Functions, J. Math. Phys., Vol. 22, 1981, pp. 2472-2481. | MR 640653 | Zbl 0471.40005

J. Ash, On the Classical Limit of Berry's Phase Integrable Systems, Commun. Math. Phys., Vol. 127, 1990, pp. 637-651. | MR 1040900 | Zbl 0698.58026

J.E. Avron, R. Seiler and L.G. Yaffe, Adiabatic Theorems and Applications to the Quantum Hall Effect, Commun. Math. Phys., Vol. 110, 1987, pp. 33-49. | MR 885569 | Zbl 0626.58033

J.E. Avron, L. Sadun and B. Simon, Chern Numbers, Quaternions and Berry's Phases in Fermi Systems, Commun. Math. Phys., Vol. 124, 1989, pp. 595-627. | MR 1014116 | Zbl 0830.57020

E. Balslev and J.M. Combes, Special Properties of Many Body Schrödinger Operators with Dilation Analytic Interactions, Commun. Math. Phys., Vol. 22, 1971, pp. 280-294. | MR 345552 | Zbl 0219.47005

V. Béletski, Essais sur le mouvement des corps cosmiques Mir, Moscow, 1977.

M.V. Berry, Quantal Phase Factors Accompanying Adiabatic Changes, Proc. R. Soc. London, Vol. A392, 1984, pp. 45-57. | MR 738926

M.V. Berry, Classical Adiabatic Angles and Quantal Adiabatic Phase, J. Phys. A: Math. Gen., Vol. 18, 1985, pp. 15-27. | MR 777620 | Zbl 0569.70020

M.V. Berry, The Quantum Phase, Five Years After, Geometric Phases in Physics, A. Shapere and F. Wilczek eds., World Scientific, Singapore, 1989, pp. 7-28. | MR 1084386

G. Gérard and D. Robert, On the Semiclassical Asymptotics of Berry's Phase, Preprint, École Polytechnique, Paris, 1989.

S. Golin, A. Knauf and S. Marmi, The Hannay Angles: Geometry, Adiabaticity and an Example, Commun. Math. Phys., Vol. 123, 1989, pp. 95-122. | MR 1002034 | Zbl 0825.58012

S. Golin and S. Marmi, Symmetries, Hannay Angles and Precession of Orbits, Europhys. Lett., Vol. 8, 1989, pp. 399-404.

S. Golin and S. Marmi, A Class of Systems with Measurable Hannay Angles, Nonlinearity, Vol. 3, 1990, pp. 507-518. | MR 1054585 | Zbl 0713.70017

L.S. Gradshteyn and I.M. Rykhik, Table of integrals, Series and Products Academic Press, London, 1980.

S. Graffi and V. Grecchi, Resonances in the Stark Effect and Perturbation Theory, Commun. Math. Phys., Vol. 62, 1978, pp. 83-96. | MR 506369

S. Graffi, V. Grecchi and E.M. Harrel Ii and H.J. Silverstone, The 1/R Expansion for H2+: Analiticity, Summability and Asymptotics, Ann. Phys., Vol. 165, 1985, pp. 441- 483. | MR 816800 | Zbl 0614.46068

J.H. Hannay, Angle Variable Holonomy in Adiabatic Excursion of an Integrable Hamiltonian, J. Phys. A: Math. Gen., Vol. 18, 1985, pp. 221-230. | MR 784910

I.W. Herbst, Dilation Analyticity in Constant Electric Field I. The Two Body Problem, Commun. Math. Phys., Vol. 64, 1979, pp. 279-298. | MR 520094 | Zbl 0447.47028

I.W. Herbst, Schrödinger Operators with External Homogeneous Electric and Magnetic Fields, NATO Advanced Studies Institute, Vol. 32B, A. Velo and A. Wightman eds.. 1982.

W. Hunziker, Schrödinger Operatrs with Electric or Magnetic Fields, in Mathematical Problems in Theoretical Physics, Lect. Notes Phys., Vol. 116, K. Osterwalder ed., Springer-Verlag, Berlin, 1979, pp. 25-44. | MR 582602 | Zbl 0471.47010

W. Hunziker and C.A. Pillet, Degenerate Asymptotic Perturbation Theory, Commun. Math. Phys., Vol. 90, 1983, pp. 219-233. | MR 714435 | Zbl 0522.47011

W. Hunziker and E. Vock, Stability of Schrödinger Eigenvalue Problems, Commun. Math. Phys., Vol. 83, 1982, pp. 281-302. | MR 649163 | Zbl 0528.35023

R. Jackiw, Berry's Phase - Topological Ideas from Atomic, Molecular and Optical Physics, Commun. Atom. Mol. Phys., Vol. 21, 1988, pp. 71-82.

T. Kato, On the Adiabatic Theorem in Quantum Mechanics, J. Phys. Soc. Japan, Vol. 5, 1950, pp. 435-439.

Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1966, L. Landau and E. Lifchitz, Mécanique Quantique Mir, Moscow, 1966. | MR 203473 | Zbl 0148.12601

P. Lochak and C. Meunier, Multiphase Averaging for Classical Systems With Applications to Adiabatic Theorems, Springer-Verlag, Berlin, 1988,. | MR 959890 | Zbl 0668.34044

J.E. Marsden, R. Montgomery and T. Ratiu, Cartan-Hannay-Berry Phases and Symmetry, Contemp. Math. A.M.S., Vol. 97, 1989, pp. 179-196. | MR 1021042 | Zbl 0694.70008

R. Montgomery, The Connection Whose Holonomy is the Classical Adiabatic Angles of Hannay and Berry and its Generalization to the Non-integrable Case, Commun. Math. Phys., Vol. 120, 1988, pp. 269-294. | MR 973536 | Zbl 0689.58043

J.P. Ramis, Dévissage Gevrey, Astérisque, Vol. 59-60, 1978, pp. 173-204. | MR 542737 | Zbl 0409.34018

J.P. Ramis, Les séries k-sommables et leurs applications, Springer, Lect. Notes Phys., Vol. 126, 1980, pp. 178-199. | MR 579749

M. Reed and B. Simons, Methods of Modern Mathematical Physics, IV. Analysis of Operators, Academic Press, New York, 1978. | MR 493421 | Zbl 0401.47001

A. SHAPERE and E. WILCZEK eds., Geometric Phases in Physics, World Scientific, Singapore, 1989. | MR 1084385 | Zbl 0914.00014

B. Simon, Holonomy, the Quantum Adiabatic Theorem and Berry's Phase, Phys. Rev. Lett., Vol. 51, 1983, pp. 2167-2170. | MR 726866

W. Thirring, A course in Mathematical Physics 1. Classical Dynamical Systems, Springer-Verlag, New York, Wien, 1978. | MR 587314 | Zbl 0387.70001

W. Thirring, A course in Mathematical Physics 3. Quantum Mechanics of Atoms and Molecules, Springer-Verlag, New York, Wien, 1981. | MR 625662 | Zbl 0462.46046

A. Weinstein, Connections of Berry and Hannay Type for Moving Lagrangian Manifolds, Adv. Math., Vol. 82, 1990, pp. 133-159. | MR 1063955 | Zbl 0713.58015