The phase diagram of the multi-dimensional Anderson localization via
analytic determination of Lyapunov exponents |
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Authors: | Email author" target="_blank">V N?KuzovkovEmail author W?von Niessen |
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Institution: | (1) Institute of Solid State Physics, University of Latvia, 8 Kengaraga Street, LV –, 1063 RIGA, Latvia;(2) Institut für Physikalische und Theoretische Chemie, Technische Universität Braunschweig, Hans-Sommer-Strasse 10, 38106 Braunschweig, Germany |
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Abstract: | The method proposed by the present authors to deal analytically
with the problem of Anderson localization via disorder J. Phys.:
Condens. Matter 14, 13777 (2002)] is generalized for higher
spatial dimensions D. In this way the generalized Lyapunov
exponents for diagonal correlators of the wave function,
2n,m , can be calculated analytically and
exactly. This permits to determine the phase diagram of the
system. For all dimensions D > 2 one finds intervals in the
energy and the disorder where extended and localized states
coexist: the metal-insulator transition should thus be interpreted
as a first-order transition. The qualitative differences permit to
group the systems into two classes: low-dimensional systems
(2 D 3), where localized states are always
exponentially localized and high-dimensional systems (D
Dc=4), where states with non-exponential localization are also
formed. The value of the upper critical dimension is found to be
D0=6 for the Anderson localization problem; this value is also
characteristic of a related problem – percolation. |
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Keywords: | |
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