Scarring by homoclinic and heteroclinic orbits

Abstract

In addition to the well known scarring effect of periodic orbits, we show here that homoclinic and heteroclinic orbits, which are cornerstones in the theory of classical chaos, also scar eigenfunctions of classically chaotic systems when associated closed circuits in phase space are properly quantized, thus introducing strong quantum correlations. The corresponding quantization rules are also established. This opens the door for developing computationally tractable methods to calculate eigenstates of chaotic systems.

5 pages, 4 figures

References in corpus (9)

• High-Power Directional Emission from Microlasers with Chaotic Resonators
• Ray and wave chaos in asymmetric resonant optical cavities
• Recent Developments in the Theory of Scarring
• Semiclassical Theory of Short Periodic Orbits in Quantum Chaos
• Semiclassical quantization with short periodic orbits
• Orbit bifurcations and the scarring of wavefunctions
• Signatures of homoclinic motion in quantum chaos
• Localization properties of groups of eigenstates in chaotic systems
• Classical invariants and the quantization of chaotic systems

Cited by in corpus (14)

• Ubiquitous quantum scarring does not prevent ergodicity
• Quantum chaotic resonances from short periodic orbits
• Scarring in open quantum systems
• The Poincare-Birkhoff theorem in Quantum Mechanics
• Quantum scarring in a spin-boson system: fundamental families of periodic orbits
• Short periodic orbit approach to resonances and the fractal Weyl law
• 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
• Formation, prevalence, and stability of bouncing-ball quantum scars
• Semiclassical basis sets for the computation of molecular vibrational states
• Variational Scarring in Open Two-Dimensional Quantum Dots
• Homoclinic Signatures of Dynamical Localization
• The scar mechanism revisited