Chaos and exponentially localized eigenstates in smooth Hamiltonian systems

We present numerical evidence to show that the wave functions of smooth classically chaotic Hamiltonian systems scarred by certain simple periodic orbits are exponentially localized in the space of unperturbed basis states. The degree of localization, as measured by the information entropy, is shown to be correlated with the local phase-space structure around the scarring orbit. Sharp localization is observed when the orbit scarring the wave function undergoes a pitchfork bifurcation and loses stability.