Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2009-09-10
J. Phys. A: Math. Theor. 42 (2009) 475007
Physics
Condensed Matter
Disordered Systems and Neural Networks
9 pages, 4 figures
Scientific paper
10.1088/1751-8113/42/47/475007
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 $T_2(L) \sim 1/L^{\kappa}$ behaves as $L^{\Phi_2(\kappa)}$, where the multifractal spectrum $\Phi_2(\kappa)$ for fermions is different from the common multifractal spectrum concerning distinguishable particles and bosons. However in the three cases, the typical transmission $T_2^{typ}(L)$ is governed by the same exponent $\kappa_2^{typ}$, which is much smaller than the naive expectation $2\kappa_1^{typ}$, where $\kappa_1^{typ}$ is the typical exponent of the one-particle transmission $T_1(L)$.
Garel Thomas
Monthus Cecile
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