TABLE OF CONTENTS For several years, scientists have sought to establish a correspondence between chaotic classical systems and their quantum correspondent, as well as criteria allowing to decide if a quantum system expresses, or not, a chaotic behaviour: irregularity of the spectra [Percival (1973); Berry (1977)], sensitivity of the spectrum over the small disturbances [Pomphrey (1974); Gr maud & al (1993)], distributions of the energy levels [Tabor (1977); Mcdonald & Kaufmann (1979)], or structures of the stationary states [Heller (1984); Mcdonald & Kaufmann (1979) ] However other authors have doubts about the existence of quantum chaos [Ford (1989); Ford & Ilg (1992); Ford & Mantica (1992)], and point out the fact that even if quantum systems express a particular behaviour when their traditional equivalent is chaotic, there are serious reasons to think that quantum chaos does not exist.
Indeed, it has already been established that the finished and closed quantum systems do not express a chaotic behaviour [Ford & Ilg (1992)]. However the principal objection about the existence of quantum chaos remains the linearity of the Schr dinger equation, which makes it insensitive over "the exponential instability of initial conditions" [Ford & Ilg (1992); Dando & Monteiro (1994)], sine qua non condition of chaos. In addition, criteria of recognition of traditional chaos stand in the concept of trajectory. However the Heisenberg principle of uncertainty excludes the possibility of defining a trajectory in quantum mechanics (see in particular the objections of Ford & Mantica (1992)).
In addition, we lack...
