Anatomy of quantum chaotic eigenstates

Stéphane Nonnenmacher (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

The eigenfunctions of quantized chaotic systems cannot be described by explicit formulas, even approximate ones. This survey summarizes (selected) analytical approaches used to describe these eigenstates, in the semiclassical limit. The levels of description are macroscopic (one wants to understand the quantum averages of smooth observables), and microscopic (one wants informations on maxima of eigenfunctions, "scars" of periodic orbits, structure of the nodal sets and domains, local correlations), and often focusses on statistical results. Various models of "random wavefunctions" have been introduced to understand these statistical properties, with usually good agreement with the numerical data. We also discuss some specific systems (like arithmetic ones) which depart from these random models.

Mots clés: quantum chaos; quantum ergodicity; random wavefunctions

Domaines: Systèmes dynamiques [math.DS]; Physique mathématique [math-ph]; Physique mathématique [math-ph]; Dynamique Chaotique [nlin.CD]; Equations aux dérivées partielles [math.AP]

Stéphane Nonnenmacher. Anatomy of quantum chaotic eigenstates. 2010. ⟨hal-00486062v1⟩