Münster 1999 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Downloads | Hilfe
TT: Tiefe Temperaturen
TT 21: Postersitzung III: Hochfrequenzeigenschaften (1-4), Amorphe Systeme (5-9), Borkarbide (10-18), Quantenflüssigkeiten (19-25), Dünne Filme (26-49), Vortexdynamik, Pinning (50-63), M-I-Überg
änge, quantenkritische Ph
änomene (64-89)
TT 21.86: Poster
Donnerstag, 25. März 1999, 14:30–18:00, Foy
Short-range plasma model for intermediate spectral statistics — •Ulrich Gerland1, Eugene Bogomolny2, and Charles Schmit2 — 1Institut für Theoretische Festkörperphysik, Universität Karlsruhe, Postfach 6980, 76128 Karlsruhe
— 2Division de Physique Théorique, Institut de Physique Nucléaire, 91406 Orsay Cedex, France
We propose a plasma model for spectral statistics displaying level repulsion without long-range spectral rigidity, i.e. statistics intermediate between random matrix and Poisson statistics as is found numerically e.g. at the critical point of the Anderson metal-insulator transition in disordered systems and in certain dynamical systems. The model emerges from Dysons one-dimensional gas corresponding to the eigenvalue distribution of the classical random matrix ensembles by restricting the logarithmic pair interaction to a finite number k of nearest neighbours. We calculate analytically the spacing distributions and the two-level statistics. In particular we show that the number variance has the simple asymptotic form Σ2(L)∼χ L for large L with χ=1/(kβ+1), where β is the inverse temperature of the gas (β=1, 2 and 4 for the orthogonal, unitary and symplectic symmetry class respectively). We also investigate the spectral statistics of several pseudointegrable systems numerically and find that for a subclass of these systems they are well described by the plasma model with k=1, β=1.