Statistical properties of two-particle transmission at Anderson transition

Cecile Monthus; Thomas Garel

doi:10.1088/1751-8113/42/47/475007

paper

Statistical properties of two-particle transmission at Anderson transition

arXiv:0909.1894 · doi:10.1088/1751-8113/42/47/475007

Abstract

The ensemble of $L \times L$ power-law random banded matrices, where the random hopping $H_{i, j}$ decays as a power-law $(b /∣ i - j ∣)^{a}$ , is known to present an Anderson localization transition at $a = 1$ , where one-particle eigenfunctions are multifractal. Here we study numerically, at this critical point, the statistical properties of the transmission $T_{2}$ for two distinguishable particles, two bosons or two fermions. We find that the statistics of $T_{2}$ is multifractal, i.e. the probability to have $T_{2} (L) \sim 1/ L^{κ}$ behaves as $L^{Φ_{2} (κ)}$ , where the multifractal spectrum $Φ_{2} (κ)$ for fermions is different from the common multifractal spectrum concerning distinguishable particles and bosons. However in the three cases, the typical transmission $T_{2}^{t y p} (L)$ is governed by the same exponent $κ_{2}^{t y p}$ , which is much smaller than the naive expectation $2 κ_{1}^{t y p}$ , where $κ_{1}^{t y p}$ is the typical exponent of the one-particle transmission $T_{1} (L)$ .

arXiv comment9 pages, 4 figures

Statistical properties of two-particle transmission at Anderson transition

Abstract

References in corpus (46)