Pure State Correlations: Chords in Phase Space

Abstract

The intensity of the overlap of a quantum state with all its phase space translations defines its quantum correlations. In the case of pure states, these are invariant with respect to Fourier transformation. The overlaps themselves are here studied in terms of the Wigner function and its Fourier transform, i.e., the characteristic function or chord function. Unlike the Wigner function, the chord function need not be real, but eventual symmetry with respect to reflections about a phase space point may relate these representations. Semiclassical approximations for the "classical-like" region of small chords and for large chords are derived. These lead to an interpretation of the Fourier invariance in terms of conjugate chords. The interrelation of large and small (sub-Planck) phase space structures previously noted in the literature are thus reinterpreted.

16 pages, 4 figures

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Cited by in corpus (12)

• Sub-Planck phase-space structures and Heisenberg-limited measurements
• Semiclassical theory for small displacements
• Husimi-Wigner representation of chaotic eigenstates
• Representation of superoperators in double phase space
• Blind spots between quantum states
• Negativity witness for the quantum ergodic conjecture
• Translations and reflections on the torus: Identities for discrete Wigner functions and transforms
• Local quantum ergodic conjecture
• Parametric Competition in non-autonomous Hamiltonian Systems
• Physical properties of the Schur complement of local covariance matrices
• Energy transitions driven by phase space reflection operators
• Classicalization by phase space measurements