title: Nodal domains statistics: a criterion for quantum chaos.
abstract: We consider the distribution of the (properly normalized) numbers of nodal domains of wave functions in 2D quantum billiards. We show that these distributions distinguish clearly between systems with integrable (separable) or chaotic underlying classical dynamics, and for each case the limiting distribution is universal (system independent). Thus, a new criterion for quantum chaos is provided by the statistics of the wave functions, which complements the well-established criterion based on spectral statistics.
authors.affiliation: The Weizmann Institute of Science, 76100 Rehovot, Israel.
authors.forename: Galya
authors.initials: G
authors.lastname: Blum
authors.forename: Sven
authors.initials: S
authors.lastname: Gnutzmann
authors.forename: Uzy
authors.initials: U
authors.lastname: Smilansky