Emergent Behaviors of Quantum Lohe Oscillators with All-to-All Coupling

Abstract

We study an emergent synchronous behavior for an ensemble of Lohe qubit oscillators whose quantum states are described by 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).