THE INTERBAND LIGHT-ABSORPTION COEFFICIENT IN THE WEAK DISORDER REGIME - AN ASYMPTOTICALLY EXACTLY SOLVABLE MODEL

We consider the interband light absorption coefficient (ILAC) for a d- dimensional discrete disordered system, whose Hamiltonian consist of a translation invariant part (d-dimensional discrete Laplacian) and an off-diagonal random part. Assuming that the range R of the latter is l arge and that its magnitude is of the order R(-d/2) we find that R = i nfinity limit of the ILAC. We discuss some properties of the ILAC in t his limit: its boundedness, edge singularities, its singular form in t he limits of vanishingly translationally invariant part or infinite ra ndom part. We also show that the latter property is the same for the s ystem with a diagonal smoothly distributed disorder, i.e. for the disc rete Schrodinger operator whose random potential has a smooth probabil ity distribution. This should be contrasted with the integrated densit y of states which is always smoother than the distribution of the rand om potential.