Classical bifurcations and entanglement in smooth Hamiltonian system

TL;DR

This paper investigates how entanglement in coupled quartic oscillators correlates with classical chaos and bifurcations, revealing nuanced relationships between quantum entanglement, classical dynamics, and localization phenomena.

Contribution

It demonstrates the influence of classical bifurcations on quantum entanglement and explores the connection between entanglement measures and localization in quantum chaos.

Findings

Entanglement increases with classical chaos parameter.

Entanglement shows minima near pitchfork bifurcations.

Entanglement shows maxima near anti-pitchfork bifurcations.

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.