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The random phase property and the Lyapunov Spectrum for disordered multichannel systems
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Roemer, Rudolf A. and SchulzBaldes, H.. (2010) The random phase property and the Lyapunov Spectrum for disordered multichannel systems. Journal of Statistical Physics, Vol.140 (No.1). pp. 122153. ISSN 00224715
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Official URL: http://dx.doi.org/10.1007/s1095501099868
Abstract
A random phase property establishing in the weak coupling limit a link between quasionedimensional random Schrödinger operators and full random matrix theory is advocated. Briefly summarized it states that the random transfer matrices placed into a normal system of coordinates act on the isotropic frames and lead to a Markov process with a unique invariant measure which is of geometric nature. On the elliptic part of the transfer matrices, this measure is invariant under the unitaries in the hermitian symplectic group of the universality class under study. While the random phase property can up to now only be proved in special models or in a restricted sense, we provide strong numerical evidence that it holds in the Anderson model of localization. A main outcome of the random phase property is a perturbative calculation of the Lyapunov exponents which shows that the Lyapunov spectrum is equidistant and that the localization lengths for large systems in the unitary, orthogonal and symplectic ensemble differ by a factor 2 each. In an AndersonAndo model on a tubular geometry with magnetic field and spinorbit coupling, the normal system of coordinates is calculated and this is used to derive explicit energy dependent formulas for the Lyapunov spectrum.
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics  
Divisions:  Faculty of Science > Centre for Scientific Computing Faculty of Science > Physics 

Library of Congress Subject Headings (LCSH):  Localization theory, Mesoscopic phenomena (Physics), Lyapunov exponents, Schrödinger operator, Markov processes, Stochastic processes  
Journal or Publication Title:  Journal of Statistical Physics  
Publisher:  Springer New York LLC  
ISSN:  00224715  
Official Date:  14 May 2010  
Dates: 


Volume:  Vol.140  
Number:  No.1  
Page Range:  pp. 122153  
Identifier:  10.1007/s1095501099868  
Status:  Peer Reviewed  
Access rights to Published version:  Restricted or Subscription Access  
References:  [And] P. W. Anderson, Absence of diffusion in certain random lattices , Phys. Rev. 109, 1492 

URI:  http://wrap.warwick.ac.uk/id/eprint/3228 
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