Exponentiated random walks, supersymmetry and localization View Full Text


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Article Info

DATE

1988-06

AUTHORS

E. Tosatti, M. Zannetti, L. Pietronero

ABSTRACT

We examine the nature and properties of the “exponentiated random walk” one-dimensional wavefunction Ψ0=exp[−x(x)], previously introduced in the context of the supersymmetric mappings of a classical Langevin random field problem. Three main results are presented. The first is that the state Ψ0 is extended, although it is the exact groundstate of a disordered one-dimensional quantum problem. The second is that in that problem supersymmetry is neither truly unbroken, or truly broken, we call this a situation of marginal unbroken supersymmetry and identify a class of other problems with the same property. The third result is obtained by studying the local behaviour of the wave function Ψ0 by means of generalized Lyapunov exponents. Locally, Ψ0 exhibits exponential localization, with a localization length identical to that of weak localization in the 1-dimensional Anderson problem. More... »

PAGES

161-166

References to SciGraph publications

  • 1985-03. Scaling behavior of one-dimensional weakly disordered models in ZEITSCHRIFT FÜR PHYSIK B CONDENSED MATTER
  • 1984. The Fokker-Planck Equation, Methods of Solution and Applications in NONE
  • 1982. Lorentz gas and random walks in MATHEMATICAL PROBLEMS IN THEORETICAL PHYSICS
  • 1980-12. Sur le spectre des opérateurs aux différences finies aléatoires in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/bf01305733

    DOI

    http://dx.doi.org/10.1007/bf01305733

    DIMENSIONS

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