Statistical properties of two-particle transmission at an Anderson transition

Abstract

The ensemble of L × L power-law random banded matrices, where the random hopping Hi,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 T2 for two distinguishable particles, two bosons or two fermions, in the non-interacting case. We find that the statistics of T2 is multifractal, i.e. the probability to have T2(L) ∼ 1/Lκ behaves as , where the multifractal spectrum Φ2(κ) for fermions is different from the common multifractal spectrum concerning distinguishable particles and bosons. However, in the three cases, the typical transmission Ttyp2(L) is governed by the same exponent κtyp2, which is much smaller than the naive expectation 2κtyp1, where κtyp1 is the typical exponent of the one-particle transmission T1(L).