The phase diagram of the metal-insulator transition in a three dimensional quantum percolation problem is investigated numerically based on the multifractal analysis of the eigenstates. The large scale numerical simulation has been performed on syste
ms with linear sizes up to $L=140$. The multifractal dimensions, exponents $D_q$ and $alpha_q$, have been determined in the range of $0leq qleq 1$. Our results confirm that this problem belongs to the same universality class as the three dimensional Anderson model, the critical exponent of the localization length was found to be $ u=1.622pm 0.035$. The mulifractal function, $f(alpha)$, appears to be universal, however, the exponents $D_q$ and $alpha_q$ produced anomalous variations along the phase boundary, $p_c^Q(E)$.
In this work we investigate the inverse of the celebrated Bohigas-Giannoni-Schmit conjecture. Using two inversion methods we compute a one-dimensional potential whose lowest N eigenvalues obey random matrix statistics. Our numerical results indicate
that in the asymptotic limit, N->infinity, the solution is nowhere differentiable and most probably nowhere continuous. Thus such a counterexample does not exist.
Entanglement is a physical resource of a quantum system just like mass, charge or energy. Moreover it is an essential tool for many purposes of nowadays quantum information processing, e.g. quantum teleportation, quantum cryptography or quantum compu
tation. In this work we investigate an extended system of N qubits. In our system a qubit is the absence or presence of an electron at a site of a tight-binding system. Several measures of entanglement between a given qubit and the rest of the system and also the entanglement between two qubits and the rest of the system is calculated in a one-electron picture in the presence of disorder. We invoke the power law band random matrix model which even in one dimension is able to produce multifractal states that fluctuate at all length scales. The concurrence, the tangle and the entanglement entropy all show interesting scaling properties.
