Journal ArticleDOI
Emergent Behaviors of Quantum Lohe Oscillators with All-to-All Coupling
Sun-Ho Choi,Seung-Yeal Ha +1 more
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TLDR
This work provides several explicit sufficient conditions for the complete synchronization of Lohe qubit oscillators in terms of the initial condition and coupling strength and shows that for identical qu bit oscillators, the Lohe model for interacting qubits satisfies an asymptotic completeness property.Abstract:
We study an emergent synchronous behavior for an ensemble of Lohe qubit oscillators whose quantum states are described by $$2\times 2$$
unitary matrices. The quantum Lohe model can be regarded as a non-abelian and quantum generalization of the Kuramoto model for classical oscillators. For the interacting qubit system, the Lohe model can be recast as a coupled ODE system. We provide several explicit sufficient conditions for the complete synchronization of Lohe qubit oscillators in terms of the initial condition and coupling strength. We also show that for identical qubit oscillators, the Lohe model for interacting qubits satisfies an asymptotic completeness property. Our analytical results confirm the numerical results from Lohe (J Phys A Math Theor 43:465301, 2010).read more
Citations
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Journal ArticleDOI
The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)
TL;DR: In this paper, the authors describe the rules of the ring, the ring population, and the need to get off the ring in order to measure the movement of a cyclic clock.
Journal ArticleDOI
On the Relaxation Dynamics of Lohe Oscillators on Some Riemannian Manifolds
TL;DR: In this paper, the collective relaxation dynamics appearing in weakly coupled Lohe oscillators in a large coupling regime were studied for a generic initial configuration via the detailed analysis on the order parameter measuring the modulus of the centroid.
Journal ArticleDOI
On the Emergence and Orbital Stability of Phase-Locked States for the Lohe Model
TL;DR: In this article, the emergence and orbital stability of phase-locked states of the Lohe model was studied and an analytical framework to confirm Lohe's observations of emergent phaselocked states was provided.
Journal ArticleDOI
Emergent Dynamics of a Generalized Lohe Model on Some Class of Lie Groups
TL;DR: In this article, the authors introduce a Lohe group which is a new class of matrix Lie groups and present a continuous dynamical system for the synchronization of group elements in a group.
References
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Book
Synchronization: A Universal Concept in Nonlinear Sciences
TL;DR: This work discusseschronization of complex dynamics by external forces, which involves synchronization of self-sustained oscillators and their phase, and its applications in oscillatory media and complex systems.
Journal ArticleDOI
The quantum internet
TL;DR: In this paper, the authors proposed a method for quantum interconnects, which convert quantum states from one physical system to those of another in a reversible manner, allowing the distribution of entanglement across the network and teleportation of quantum states between nodes.
Journal ArticleDOI
The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)
TL;DR: In this paper, the authors describe the rules of the ring, the ring population, and the need to get off the ring in order to measure the movement of a cyclic clock.
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