Falko, Vladimir and Efetov, K. B. (1995) Statistics of prelocalized states in disordered conductors. Physical review B, 52 (24). pp. 1741317429. ISSN 01631829

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Abstract
The distribution function of local amplitudes, t = \psi(r(0))\(2), of singleparticle states in disordered conductors is calculated on the basis of a reduced version of the supersymmetric sigma model solved using the saddlepoint method. Although the distribution of relatively small amplitudes can be approximated by the universal PorterThomas formulas known from the randommatrix theory, the asymptotical statistics of large t's is strongly modified by localization effects. In particular, we find a multifractal behavior of eigenstates in twodimensional (2D) conductors which follows from the noninteger powerlaw scaling for the inverse participation numbers (IPN's) with the size of the system, Vt(n) proportional to L((n1)d*(n)), where d*(n) = 2  beta(1)n/(4 pi nu D) is a function of the index n and disorder. The result is valid for all fundamental symmetry classes (unitary, beta(u) = 1; orthogonal, beta(o) = 1/2; symplectic, beta(s) = 2). The multifractality is due to the existence of prelocalized states which are characterized by a powerlaw form of statistically averaged envelopes of wave functions at the tails, \psi(t)(r)\(2) proportional to r(2 mu), mu = mu(t) < 1. The prelocalized states in short quasionedimensional (1D) wires have the tails \psi(x)\(2) proportional to x(2), too, although their IPN's indicate no fractal behavior. The distribution function of the largestamplitude fluctuations of wave functions in 2D and 3D conductors has logarithmically normal asymptotics.
Item Type:  Journal Article 

Journal or Publication Title:  Physical review B 
Additional Information:  © 1995 The American Physical Society 
Uncontrolled Keywords:  /dk/atira/pure/researchoutput/libraryofcongress/qc 
Subjects:  
Departments:  Faculty of Science and Technology > Physics 
ID Code:  57077 
Deposited By:  ep_importer_pure 
Deposited On:  05 Sep 2012 16:39 
Refereed?:  Yes 
Published?:  Published 
Last Modified:  15 Nov 2019 01:45 
URI:  https://eprints.lancs.ac.uk/id/eprint/57077 
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