Energy level dynamics in systems with weakly multifractal eigenstates: Equivalence to onedimensional correlated fermions at low temperatures
Abstract
It is shown that the parametric spectral statistics in the critical random matrix ensemble with multifractal eigenvector statistics are identical to the statistics of correlated onedimensional (1D) fermions at finite temperatures. For weak multifractality the effective temperature of fictitious 1D fermions is proportional to T_{eff}~(1d_{n})/n<<1, where d_{n} is the fractal dimension found from the nth moment of the inverse participation ratio. For large energy and parameter separations the fictitious fermions are described by the Luttinger liquid model which follows from the CalogeroSutherland model. The lowtemperature asymptotic form of the twopoint equalparameter spectral correlation function is found for all energy separations and its relevance for the lowtemperature equaltime density correlations in the CalogeroSutherland model is conjectured.
 Publication:

Physical Review B
 Pub Date:
 October 2000
 DOI:
 10.1103/PhysRevB.62.9888
 arXiv:
 arXiv:condmat/0002120
 Bibcode:
 2000PhRvB..62.9888K
 Keywords:

 72.15.Rn;
 72.20.Ht;
 72.70.+m;
 73.23.b;
 Localization effects;
 Highfield and nonlinear effects;
 Noise processes and phenomena;
 Electronic transport in mesoscopic systems;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 4 pages, Revtex, final journal version