Distribution of the local density of states, reflection coefficient and Wigner delay time in absorbing ergodic systems at the point of chiral symmetry

Employing the chiral Unitary Ensemble of random matrices we calculate the probability distribution of the local density of states for zero-dimensional ("quantum chaotic") two-sublattice systems at the point of chiral symmetry E=0 and in the presence of uniform absorption. The obtained result can be used to find the distributions of the reflection coefficent and of the Wigner time delay for such systems.