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 $D_q$ are non-fluctuating quantities, contrary to a recent claim in the literature. A recently proposed relation between $D_2$ and the spectral compressibility $\chi$ is violated in the regime of strong multifractality, with $\chi\to 1$ in the limit $D_2\to 0$.Comment: 4 pages, 3 eps figure

Zero-frequency anomaly in quasiclassical ac transport: Memory effects in a two-dimensional metal with a long-range random potential or random magnetic field

We study the low-frequency behavior of the {\it ac} conductivity $\sigma(\omega)$ of a two-dimensional fermion gas subject to a smooth random potential (RP) or random magnetic field (RMF). We find a non-analytic $\propto|\omega|$ correction to ${\rm Re} \sigma$, which corresponds to a $1/t^2$ long-time tail in the velocity correlation function. This contribution is induced by return processes neglected in Boltzmann transport theory. The prefactor of this $|\omega|$-term is positive and proportional to $(d/l)^2$ for RP, while it is of opposite sign and proportional to $d/l$ in the weak RMF case, where $l$ is the mean free path and $d$ the disorder correlation length. This non-analytic correction also exists in the strong RMF regime, when the transport is of a percolating nature. The analytical results are supported and complemented by numerical simulations.Comment: 12 pages, RevTeX, 7 figure

Strong magnetoresistance induced by long-range disorder

We calculate the semiclassical magnetoresistivity $\rho_{xx}(B)$ of non-interacting fermions in two dimensions moving in a weak and smoothly varying random potential or random magnetic field. We demonstrate that in a broad range of magnetic fields the non-Markovian character of the transport leads to a strong positive magnetoresistance. The effect is especially pronounced in the case of a random magnetic field where $\rho_{xx}(B)$ becomes parametrically much larger than its B=0 value.Comment: REVTEX, 4 pages, 2 eps figure

Nonadiabatic scattering of a quantum particle in an inhomogenous magnetic field

We investigate the quantum effects, in particular the Landau-level quantization, in the scattering of a particle the nonadiabatic classical dynamics of which is governed by an adiabatic invariant. As a relevant example, we study the scattering of a drifting particle on a magnetic barrier in the quantum limit where the cyclotron energy is much larger than a broadening of the Landau levels induced by the nonadiabatic transitions. We find that, despite the level quantization, the exponential suppression $\exp(-2\pi d/\delta)$ (barrier width $d$, orbital shift per cyclotron revolution $\delta$) of the root-mean-square transverse displacement experienced by the particle after the scattering is the same in the quantum and the classical regime.Comment: 4 page

Surface criticality and multifractality at localization transitions

We develop the concept of surface multifractality for localization-delocalization (LD) transitions in disordered electronic systems. We point out that the critical behavior of various observables related to wave functions near a boundary at a LD transition is different from that in the bulk. We illustrate this point with a calculation of boundary critical and multifractal behavior at the 2D spin quantum Hall transition and in a 2D metal at scales below the localization length.Comment: Published versio

Exact relations between multifractal exponents at the Anderson transition

Two exact relations between mutlifractal exponents are shown to hold at the critical point of the Anderson localization transition. The first relation implies a symmetry of the multifractal spectrum linking the multifractal exponents with indices $q1/2$. The second relation connects the wave function multifractality to that of Wigner delay times in a system with a lead attached.Comment: 4 pages, 3 figure

Comparison of seeded and vegetatively propagated bermudagrass

Last updated: 10/19/201