DENSITY-OF-STATES FOR A WEAKLY COUPLED DISORDERED ARRAY

A technique for the calculation of the density of states for a one-dim ensional array of rectangular quantum wells in the weak-coupling limit is described, at various degrees of disorder. It is found that in the limit that the degree of disorder grows large, the smooth component o f the density of states of this configuration is well approximated by the polynomial function D(E)=7.4-1.8epsilon+0.50epsilon2-0.098epsilon3 , where epsilon represents the absolute value of energy measured in un its of 10(-4)h2BAR/2ma2, m is particle mass, and a is well width. The function D(E) exhibits a localization of energies at the maximum bound -state energy epsilon = 0. A calculation is included which addresses t he distribution of nearest-neighbor spacings of energies for the prese nt configuration. The distribution obtained illustrates strong attract ion between eigenvalues and is found to be well approximated by an exp onential (Poissonian) fit.