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Register a new userScattering at the Anderson transition: Power--law banded random matrix model
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Added by
J. A. Mendez-Bermudez
Publication date
2006
fields
Physics
and research's language is
English
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We analyze the scattering properties of a periodic one-dimensional system at criticality represented by the so-called power-law banded random matrix model at the metal insulator transition. We focus on the scaling of Wigner delay times $tau$ and resonance widths $Gamma$. We found that the typical values of $tau$ and $Gamma$ (calculated as the geometric mean) scale with the system size $L$ as $tau^{tiny typ}propto L^{D_1}$ and $Gamma^{tiny typ} propto L^{-(2-D_2)}$, where $D_1$ is the information dimension and $D_2$ is the correlation dimension of eigenfunctions of the corresponding closed system.
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We investigate the wave-packet dynamics of the power-law bond disordered one-dimensional Anderson model with hopping amplitudes decreasing as $H_{nm}propto |n-m|^{-alpha}$. We consider the critical case ($alpha=1$). Using an exact diagonalization scheme on finite chains, we compute the participation moments of all stationary energy eigenstates as well as the spreading of an initially localized wave-packet. The eigenstates multifractality is characterized by the set of fractal dimensions of the participation moments. The wave-packet shows a diffusive-like spread developing a power-law tail and achieves a stationary non-uniform profile after reflecting at the chain boundaries. As a consequence, the time-dependent participation moments exhibit two distinct scaling regimes. We formulate a finite-size scaling hypothesis for the participation moments relating their scaling exponents to the ones governing the return probability and wave-function power-law decays.
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