# Scarring by homoclinic and heteroclinic orbits.

@article{Wisniacki2006ScarringBH, title={Scarring by homoclinic and heteroclinic orbits.}, author={Diego Wisniacki and Eduardo G Vergini and Rosa M. Benito and Florentino Borondo}, journal={Physical review letters}, year={2006}, volume={97 9}, pages={ 094101 } }

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…

## 29 Citations

Quantum localization through interference on homoclinic and heteroclinic circuits

- Physics
- 2008

Localization effects due to scarring constitute one of the clearest indications of the relevance of interference in the transport of quantum probability density along quantized closed circuits in…

Short periodic orbit approach to resonances and the fractal Weyl law.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

Solid numerical evidence is provided, for the paradigmatic systems of the open baker and cat maps, that by using the semiclassical short periodic orbit approach the dimensionality of the eigenvalue problem is reduced according to the fractal Weyl law.

Homoclinic signatures of dynamical localization

- Physics
- 2007

It is demonstrated that the oscillations in the width of the momentum distribution of atoms moving in a phase-modulated standing light field, as a function of the modulation amplitude λ, are…

Does scarring prevent ergodicity

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- 2020

Classically chaotic systems are ergodic, that is after a long time, any trajectory will be arbitrarily close to any point of the available phase space, filling it uniformly. Using Born's rules to…

Classical Invariants in the Quantum Mechanics of Chaotic Systems

- Physics
- 2014

The relevance of classical invariants in the quantization and dynamics of quantum systems is discussed. Special attention is paid to the influence of periodic orbits (“scars”) and the associated…

Quantum chaotic resonances from short periodic orbits.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

The number of long-lived states produced within the formulation is in agreement with the fractal Weyl law conjectured recently in this setting, and the accuracy of the approximations is confirmed using the open quantum baker map as an example.

Poincaré-Birkhoff theorem in quantum mechanics.

- Physics, MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2011

Quantum manifestations of the dynamics around resonant tori in perturbed hamiltonian systems, dictated by the Poincaré-Birkhoff theorem, are shown to exist. They are embedded in the interactions…

Ubiquitous quantum scarring does not prevent ergodicity.

- PhysicsNature communications
- 2021

This work shows that all eigenstates of the chaotic Dicke model are actually scarred, and shows that even the most random states of this interacting atom-photon system never occupy more than half of the available phase space.

Quasimodes in Integrable Systems and Semi-Classical Limit

- Physics
- 2016

Quasimodes are long-living quantum states that are localized along classical orbits. They can be considered as resonances, whose wave functions display semi-classical features. In some integrable…

Breakdown mechanisms of normally hyperbolic invariant manifolds in terms of unstable periodic orbits and homoclinic/heteroclinic orbits in Hamiltonian systems

- Physics
- 2015

We analyze the mechanism of breakdown of normally hyperbolic invariant manifolds (NHIMs) based on unstable periodic orbits, homoclinic and heteroclinic orbits in NHIMs for Hamiltonian systems. First,…

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