Entanglement in quantum catastrophes

Abstract

We classify entanglement singularities for various two-mode bosonic systems in terms of catastrophe theory. Employing an abstract phase-space representation, we obtain exact results in limiting cases for the entropy in cusp, butterfly, and two-dimensional catastrophes. We furthermore use numerical results to extract the scaling of the entropy with the non-linearity parameter, and discuss the role of mixing entropies in more complex systems.

7 pages, 3 figures

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• Identifying the order of a quantum phase transition by means of Wehrl entropy in phase-space
• Caustics in quantum many-body dynamics
• Catastrophes in non-equilibrium many-particle wave functions: universality and critical scaling
• Entanglement sharing in $E\otimes \epsilon$ Jahn-Teller model in the presence of a magnetic field
• Polynomial potentials and coupled quantum dots in two and three dimensions
• Quantum catastrophes from an algebraic perspective
• Arnold's potentials and quantum catastrophes II