Absence of geometrical phases in the rotating stark effect
Annales de l'I.H.P. Physique théorique, Volume 56 (1992) no. 3, pp. 279-305.
     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},
     pages = {279--305},
     publisher = {Gauthier-Villars},
     volume = {56},
     number = {3},
     year = {1992},
     mrnumber = {1160852},
     zbl = {0757.35064},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1992__56_3_279_0/}
AU  - Caliceti, Emanuela
AU  - Marmi, Stefano
AU  - Nardini, Franco
TI  - Absence of geometrical phases in the rotating stark effect
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1992
SP  - 279
EP  - 305
VL  - 56
IS  - 3
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1992__56_3_279_0/
LA  - en
ID  - AIHPA_1992__56_3_279_0
ER  - 
%0 Journal Article
%A Caliceti, Emanuela
%A Marmi, Stefano
%A Nardini, Franco
%T Absence of geometrical phases in the rotating stark effect
%J Annales de l'I.H.P. Physique théorique
%D 1992
%P 279-305
%V 56
%N 3
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1992__56_3_279_0/
%G en
%F 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, Volume 56 (1992) no. 3, pp. 279-305. http://www.numdam.org/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 | Zbl

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

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

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

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

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

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 | Zbl

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 | Zbl

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 | Zbl

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

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

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

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 | Zbl

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 | Zbl

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

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 | Zbl

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

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

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 | Zbl

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

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

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 | Zbl

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

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 | Zbl

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 | Zbl

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

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

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

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

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

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

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

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