552 research outputs found
Fluctuations of the inverse participation ratio at the Anderson transition
Statistics of the inverse participation ratio (IPR) at the critical point of
the localization transition is studied numerically for the power-law random
banded matrix model. It is shown that the IPR distribution function is
scale-invariant, with a power-law asymptotic ``tail''. This scale invariance
implies that the fractal dimensions are non-fluctuating quantities,
contrary to a recent claim in the literature. A recently proposed relation
between and the spectral compressibility is violated in the regime
of strong multifractality, with in the limit .Comment: 4 pages, 3 eps figure
Quantum criticality and minimal conductivity in graphene with long-range disorder
We consider the conductivity of graphene with negligible
intervalley scattering at half filling. We derive the effective field theory,
which, for the case of a potential disorder, is a symplectic-class
-model including a topological term with . As a
consequence, the system is at a quantum critical point with a universal value
of the conductivity of the order of . When the effective time reversal
symmetry is broken, the symmetry class becomes unitary, and
acquires the value characteristic for the quantum Hall transition.Comment: 4 pages, 1 figur
Intensity distribution for waves in disordered media: deviations from Rayleigh statistics
We study the intensity distribution function, P(I), for monochromatic waves
propagating in quasi one-dimensional disordered medium, assuming that a point
source and a point detector are embedded in the bulk of the medium. We find
deviations from the Rayleigh statistics at moderately large I and a
logarithmically-normal asymptotic behavior of P(I). When the radiation source
and the detector are located close to the opposite edges of the sample (on a
distance much less then the sample length), an intermediate regime with a
stretched-exponential behavior of P(I) emerges.Comment: 4 pages Revtex, 3 figures included as eps file
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