NAME: K. A. Muttalib 
 
 ADDRESS: Physics Dept. 
          University of Florida
          New Physics Building
          P.O. Box 118440
          
          
 
 EMAIL ADDRESS: muttalib@phys.ufl.edu
 
 TITLE OF TALK: ``q-polynomials in random matrix theory and the
                physics of multifractality''
 
 ABSTRACT OF TALK: 

A wide variety of quantum systems (like complex nuclei, atoms and
molecules, small disordered metals as well as quantum systems whose 
classical counterparts are chaotic) share some generic statistical 
properties of energy levels. These properties can be understood most 
naturally in terms of the stochastic and symmetry properties of the
Gaussian Random Matrix Ensembles (RMEs). In this talk I will briefly 
review how the well known universal (zero parameter) limits of the 
Gaussian RMEs follow from certain double scaling limits of classical 
orthogonal polynomials. I will then discuss a new class of RMEs based 
on the q-orthogonal polynomials which describes the generic statistical
properties of quantum systems in the `critical' regime when the system
undergoes a phase transition from the chaotic to an integrable state. 
As an example, I will consider the metal to insulator transition in 
disordered electronic systems, where this new class of RMEs describe
the  expected `multifractal' wavefunctions associated with the critical 
regime. 
 
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