Collapse of the Zeeman structure of the hydrogen atom in external electric field
CHAMP ELECTRIQUE CRISTALLIN
ATOMES
HYDROGENE
STRUCTURE MAGNETIQUE
Abstract : From Zeeman to Stark structure of a weakly split Rydberg n multiplet of the H atom in parallel magnetic and electric fields is analyzed. Classical mechanics together with topologiacl and group theoretical arguments enable us to describe in details the modifications of dynamics under the variation of electric field near the point where the collapse of magntic Zeeman structure is observed. Sequence of classical bifurcations responsible for the transition between different dynamic regimes is given. Comparison with quantum picture is done.
MICHEL
SADOVSKII
SHILINSKII
P/95/86
IHES
09/1995
A4
4 f.
EN
TEXTE
PREPUBLICATION
P_95_86.pdf
1995
Extrema of P-invariant functions on the Brillouin zone
ZONES DE BRILLOUIN
THEORIE DE MORSE
MAXIMUMS ET MINIMUMS
CRISTALLOGRAPHIE
MATHEMATIQUES
SYMETRIE
PHYSIQUE
Exapnded version of a lecture fiven at Naples, on October 25, 1991 at a Colloquium in memory of Léon Vanhove
Abstract : This paper studies the number of extrema (and their positions) of a countinuous Morse function on the Brillouin zone, when it is invariant by the point group symmetry of the crystal. Forty years ago, Vanhove had shown the importance of this problem in physics, but he could use only the crystal translational symmetry. In that case Morse theory predicts at least eight extrema. With the added use of general symmetry arguments we show that this number is larger for six of the 14 classes of Bravais lattices ; moreover it is possible to give the position of the extrema (and their nature) for 30 of the 73 arithmetic classes.This paper is written for a larger audience than that of solid state physicists ; it also defines carefully the necessary crystallographic concepts which are generally poorly understood in the solid state literature.
MICHEL
P/92/16
IHES
04/1992
A4
13 f.
EN
TEXTE
PREPUBLICATION
P_92_16.pdf
1992
La Musique des sphères ou la recherche de I'harmonie chez Kepler
MATHEMATIQUES
SCIENCE
ART
PHILOSOPHIE
ASTRONOMIE
MUSIQUE
ARITHMETIQUE
GEOMETRIE
PLANETE
LOIS DE KEPLER
CARTIER
M/91/27
IHES
03/1991
A4
12 f.
FR
TEXTE
PREPUBLICATION
M_91_27.pdf
1991
Non commutative geometry and physics
GEOMETRIE NON COMMUTATIVE
C*-ALGEBRES
TOPOLOGIE
COHOMOLOGIE
THEORIE QUANTIQUE
FIBRES VECTORIELS
PHYSIQUE MATHEMATIQUE
CONNES
M/93/32
IHES
06/1993
A4
70 f.
EN
TEXTE
PREPUBLICATION
M_93_32.pdf
1993
Noncomutative geometry year 2000
GEOMETRIE NON COMMUTATIVE
THEORIE DES HAUTES ENERGIES
THEORIE DES NOMBRES
ALGEBRES D'OPERATEURS
CONNES
M/00/73
IHES
11/2000
A4
35 f.
EN
TEXTE
PREPUBLICATION
M_00_73.pdf
2000
Rydberg states of atoms and molecules. Basic group theoretical and topological analysis
ETATS DE RYDBERG
ATOMES
HYDROGENE
CHAMPS ELECTROMAGNETIQUES
Abstract : Rydberg states of atoms and molecules are studied within the qualitative approach-based primarily on topological and group theoretical analysis. The correspondence between classical and quantum mechanics is explored to apply the results of qualitative (topological) approach to classical mechanics developed by Poincaré, Lyapounov and Smale to quantum problems. The study of the action of the symmetry group of the problems considered on the classical phase space enables us to predict qualitative features of the energy level patterns for quantum Rydberg operators.
MICHEL
ZHILINSKII
P/97/54
IHES
07/1997
A4
41 f.
EN
TEXTE
PREPUBLICATION
P_97_54.pdf
1997
Tendances nouvelles en mécanique : Quatre conférences sur la mécanique céleste et les instabilités
MECANIQUE CELESTE
RELATIVITE GENERALE
EXPERIENCES
TROUS NOIRS
STABILITE
CONVECTION THERMIQUE
CARTIER
CARTER
GUYON
MARCHAL
P/79/310
IHES
11/1979
A4
15 f.
FR
TEXTE
PREPUBLICATION
P_79_310.pdf
1979