Scars of the Wigner function

Abstract

We propose a picture of Wigner function scars as a sequence of concentric rings along a two-dimensional surface inside a periodic orbit. This is verified for a two-dimensional plane that contains a classical orbit of a Hamiltonian system with two degrees of freedom. The orbit is hyperbolic and the classical Hamiltonian is ``softly chaotic'' at the energies considered. The stationary wave functions are the familiar mixture of scarred and random waves, but the spectral average of the Wigner functions in part of the plane is nearly that of a harmonic oscillator and individual states are also remarkably regular. These results are interpreted in terms of the semiclassical picture of chords and centres, which leads to a qualitative explanation of the interference effects that are manifest in the other region of the plane. The qualitative picture is robust with respect to a canonical transformation that bends the orbit plane.

6(six) pages, 6(six) postscript figures. [email protected]

References in corpus (5)

• Linear and Nonlinear Theory of Eigenfunction Scars
• Recent Developments in the Theory of Scarring
• Quantization of a billiard model for interacting particles
• Geometrical approach to the distribution of the zeroes for the Husimi function
• Scars of Invariant Manifolds in Interacting Chaotic Few-Body Systems

Cited by in corpus (8)

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• Semiclassical propagation of Wigner functions
• Nonclassical phase-space trajectories for the damped harmonic quantum oscillator
• Hyperbolic Scar Patterns in Phase Space
• Semiclassical spatial correlations in chaotic wave functions
• Time-domain scars: resolving the spectral form factor in phase space
• Husimi-Wigner representation of chaotic eigenstates
• On Bargmann Representations of Wigner Function