Quantum synchronization of the Schrödinger-Lohe model

We present a quantum synchronization estimate of the Schrödinger-Lohe (S-L) model introduced by Lohe (2010 J. Phys. A: Math. Theor. 43 465301). The S-L model describes the dynamics of quantum oscillators on the nodes of a quantum network. When the coupling strength is positive and the maximal L² distances between normalized initial wave functions are smaller than , we show that the L² distances between wave functions converge to zero exponentially fast. Our result generalizes earlier work by Chi et al (2014 J. Math. Phys. 55 052703) for the Lohe model.