Localization properties of one-dimensional speckle potentials in a box

We investigate the localization properties of the single particle spectrum of a one-dimensional speckle potential in a box. We consider both the repulsive and the attractive cases. The system is controlled by two parameters: the size of the box and a rescaled potential intensity. The latter is a function of the particle mass, the correlation length and the average intensity of the field. Depending on both these parameters values and the considered energy level, the eigenstates exhibit different regimes of localization. In order to identify the regimes for the excited states, we use a technique developed in this work. Depending on the chosen parameters values, we find that it is possible not observing any effective mobility edge nor delocalization of the eigenstates due to the finite size of the system.