Laboratoire de Physique Théorique
Toulouse - UMR 5152

We investigate how the multifractality of quantum wave functions can vary under the effect of perturbations . A one-dimensional system is used as a generic example, originated from a Hamiltonian with a singular potential. Two possible scenarii of the breakdown of multifractality are detailed. On the one hand we find that if the potential singularity is smoothed, multifractality survives below a certain scale of the quantum fluctuations. This is clearly in agreement with previous studies of Anderson-type transition where the multifractality can be found close to the critical point. On the other hand, for example in a small deformation of the basis, the fluctuations of the wave functions are changed at every scale and each multifractal exponent smoothly goes to the corresponding value for delocalised states.