title: Universal relationship between a quantum phase transition and instability points of classical systems.
abstract: The direct and universal relationship between the accumulation of exceptional points in the quantum spectrum at a phase transition and the singularity of the classical action at a homoclinic point of the separatrix is investigated. The particular common features are the analytic structure and, related to it, instability and high sensitivity leading generically to the onset of chaos in both cases under perturbation.
authors.affiliation: Centre of Theoretical Physics and School of Physics, University of the Witwatersrand, P.O. Wits 2050, Johannesburg, South Africa.
authors.forename: W D
authors.initials: WD
authors.lastname: Heiss
authors.forename: M
authors.initials: M
authors.lastname: Müller