AMPLIFICATION AND DISORDER EFFECTS IN A KRONIG-PENNEY CHAIN OF ACTIVEPOTENTIALS

We report in this paper analytical and numeric:al results on the effec t of amplification (due to non-Hermitian site potentials) on the trans mission and reflection coefficients of a periodic one-dimensional Kron ig-Penney lattice. A qualitative agreement is found with the tight-bin ding model where the transmission and reflection increase for small sy stem lengths before strongly oscillating with a maximum at a certain l ength. For larger lengths the transmission decays exponentially at the same rate as in the growing region while the reflection saturates at a high value. However, the maximum transmission (and reflection) moves to larger system lengths and diverges in the limit of vanishing ampli fication instead of going to unity. In very large samples, it is antic ipated that the presence of disorder and the associated length scale w ill limit this uninhibited growth in amplification. Also, there are ot her interesting competitive effects of the disorder and amplification giving rise to some non-monotonic behaviour in the peak of the transmi ssion.