Using reservoir computing to construct scarred wave functions

Scar theory is one of the fundamental pillars in the field of quantum chaos, and scarred functions are a superb tool to carry out studies in it. Several methods, usually semiclassical, have been described to cope with these two phenomena. In this paper, we present an alternative method, based on the novel machine learning algorithm known as reservoir computing, to calculate such scarred wave functions together with the associated eigenstates of the system. The resulting methodology achieves outstanding accuracy while reducing execution times by a factor of ten. As an illustration of the effectiveness of this method, we apply it to the widespread chaotic two-dimensional coupled quartic oscillator.