title: Quantum chaos in one dimension?
abstract: In this work we investigate the inverse of the celebrated Bohigas-Giannoni-Schmit conjecture. Using two inversion methods we compute a one-dimensional potential whose lowest N eigenvalues obey random matrix statistics. Our numerical results indicate that in the asymptotic limit N→∞ the solution is nowhere differentiable and most probably nowhere continuous. Thus such a counterexample does not exist.
authors.affiliation: Elméleti Fizika Tanszék, Fizikai Intézet, Budapesti Műszaki és Gazdaságtudományi Egyetem, Budapest, Hungary.
authors.forename: László
authors.initials: L
authors.lastname: Ujfalusi
authors.forename: Imre
authors.initials: I
authors.lastname: Varga
authors.forename: Dániel
authors.initials: D
authors.lastname: Schumayer