Scars on Quantum Networks Ignore the Lyapunov Exponent

Abstract

We show that enhanced wave function localization due to the presence of short unstable orbits and strong scarring can rely on completely different mechanisms. Specifically we find that in quantum networks the shortest and most stable orbits do not support visible scars, although they are responsible for enhanced localization in the majority of the eigenstates. Scarring orbits are selected by a criterion which does not involve the classical stability. We obtain predictions for the energies of visible scars and the distributions of scarring strengths and inverse participation numbers.