Practical quantum synchronization for the Schrödinger–Lohe system. (19th April 2016)

• Record Type: Journal Article
• Authors: Choi, Sun-Ho; Cho, Junghee; Ha, Seung-Yeal
• Is Part Of: Journal of physics. Volume 49:Number 20(2016)
• Publication Date: 2016-04-19
• Subjects: emergence -- Kuramoto model -- Schrödinger–Lohe model -- quantum network -- quantum synchronization; 82C10 -- 82C22 -- 35B37; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/49/20/205203
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We present a practical synchronization method for the Schrödinger–Lohe (S–L) system distinct potentials. The S–L model describes the spatial-temporal evolution of the wave functions of quantum Lohe oscillators on a network with Lohe couplings. When the potential effects are ignored, complete wave function synchronization (CWFS) can emerge in the sense that the L 2 -distance between wave functions exponentially approaches zero for a class of initial wave functions. In contrast, when the Lohe oscillators are under the effect of potential forces, CWFS cannot occur. In this study, we employ a weaker concept of quantum synchronization for discussing the asymptotic collective behavior of the S–L model. This concept leads to ' practical synchronization ' of the S–L model. In practical synchronization, the L 2 -distance between wave functions can be upper bounded by the inverse power of the square root of the coupling strength; as the coupling strength increases. Thus, the L 2 -discrepancy between wave functions arbitrarily decreases as the coupling strength increases. We present a sufficient analytical framework for this practical synchronization, which is a generalization of the earlier result in (Choi S-H and Ha S-Y 2014 J. Phys. A: Math. Theor. 47 355104 )