Extended tail states in an imaginary random potential - art. no. 075114

The tail eigenstates, having an anomalously small real part of energy Re (e psilon) are considered for the non-Hermitian disordered Hamiltonian with an imaginary random potential. Unlike in the case of Hermitian quantum mechan ics, our tail states are extended over a parametrically large region. Such states appear if the values of the random potential accidentally happens to be anomalously close inside the region. Analytical results for the density of tail states are confirmed by numerical simulations.