Classical bifurcations and entanglement in smooth Hamiltonian system

Abstract

We study entanglement in two coupled quartic oscillators. It is shown that the entanglement, as measured by the von Neumann entropy, increases with the classical chaos parameter for generic chaotic eigenstates. We consider certain isolated periodic orbits whose bifurcation sequence affects a class of quantum eigenstates, called the channel localized states. For these states, the entanglement is a local minima in the vicinity of a pitchfork bifurcation but is a local maxima near a anti-pitchfork bifurcation. We place these results in the context of the close connections that may exist between entanglement measures and conventional measures of localization that have been much studied in quantum chaos and elsewhere. We also point to an interesting near-degeneracy that arises in the spectrum of reduced density matrices of certain states as an interplay of localization and symmetry.

7 pages, 6 figures

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• Quantum entanglement between a nonlinear nanomechanical resonator and a microwave field
• Non-stationary Dynamics in the Bouncing Ball: A Wavelet perspective
• Floquet states of kicked particle in a singular potential: Exponential and power-law profiles
• Symmetry Properties of Quantum Dynamical Entropy
• Signatures of nonclassical effects in tomograms
• Classical analogs of the covariance matrix, purity, linear entropy, and von Neumann entropy