Density of states for a weakly coupled disordered array

A technique for the calculation of the density of states for a one-dimensional 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 of the density of states of this configuration is well approximated by the polynomial function D(ɛ)=7.4-1.8ɛ+0.50${\mathrm{\varepsilon }}^2$-0.098${\mathrm{\varepsilon }}^3$, where ɛ represents the absolute value of energy measured in units of ${10}^{\mathrm{-}4}$${\mathrm{ħ}}^2$/2${\mathit{ma}}^2$, m is particle mass, and a is well width. The function D(ɛ) exhibits a localization of energies at the maximum bound-state energy ɛ=0. A calculation is included which addresses the distribution of nearest-neighbor spacings of energies for the present configuration. The distribution obtained illustrates strong attraction between eigenvalues and is found to be well approximated by an exponential (Poissonian) fit.