Signatures of homoclinic motion in quantum chaos

Abstract

Homoclinic motion plays a key role in the organization of classical chaos in Hamiltonian systems. In this Letter, we show that it also imprints a clear signature in the corresponding quantum spectra. By numerically studying the fluctuations of the widths of wavefunctions localized along periodic orbits we reveal the existence of an oscillatory behavior, that is explained solely in terms of the primary homoclinic motion. Furthermore, our results indicate that it survives the semiclassical limit.

5 pages, 4 figures

References in corpus (4)

• Linear and Nonlinear Theory of Eigenfunction Scars
• Orbit bifurcations and the scarring of wavefunctions
• Localization properties of groups of eigenstates in chaotic systems
• Classical invariants and the quantization of chaotic systems

Cited by in corpus (16)

• Scarring by homoclinic and heteroclinic orbits
• Quantum chaotic resonances from short periodic orbits
• Scarring in open quantum systems
• The Poincare-Birkhoff theorem in Quantum Mechanics
• Short periodic orbit approach to resonances and the fractal Weyl law
• Revealing the evolution, the stability and the escapes of families of resonant periodic orbits in Hamiltonian systems
• Using basis sets of scar functions
• Scars in Dirac fermion systems: the influence of an Aharonov--Bohm flux
• Impact of chaos on precursors of quantum criticality
• Semi-classical Scar functions in phase space
• Semiclassical basis sets for the computation of molecular vibrational states
• Superscars in the LiNC=LiCN isomerization reaction
• Homoclinic Signatures of Dynamical Localization
• Semiclassical Coherent States propagator
• The scar mechanism revisited
• Semiclassical matrix elements for a chaotic propagator in the Scar functions basis