The Wigner-Lohe model for quantum synchronization and its emergent dynamics

Paolo Antonelli; Seung-Yeal Ha; Dohyun Kim; Pierangelo Marcati; Paolo Antonelli; Seung-Yeal Ha; Dohyun Kim; Pierangelo Marcati

doi:10.3934/nhm.2017018

Networks and Heterogeneous Media

2017, Volume 12, Issue 3: 403-416. doi: 10.3934/nhm.2017018

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The Wigner-Lohe model for quantum synchronization and its emergent dynamics

1.
Gran Sasso Science Institute, viale F. Crispi, 7, 67100 L'Aquila, Italy
2.
Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Republic of Korea
3.
Korea Institute for Advanced Study, Hoegiro 87, Seoul, 130-722, Republic of Korea

Received: 01 February 2017 Revised: 01 June 2017
Primary: 35Q40; Secondary: 82C22, 93D20, 35B40

We present the Wigner-Lohe model for quantum synchronization which can be derived from the Schrödinger-Lohe model using the Wigner formalism. For identical one-body potentials, we provide a priori sufficient framework leading the complete synchronization, in which L²-distances between all wave functions tend to zero asymptotically.
- Quantum synchronization,
- emergent behavior,
- Wigner equation,
- quantum hydrodynamics
Citation: Paolo Antonelli, Seung-Yeal Ha, Dohyun Kim, Pierangelo Marcati. The Wigner-Lohe model for quantum synchronization and its emergent dynamics[J]. Networks and Heterogeneous Media, 2017, 12(3): 403-416. doi: 10.3934/nhm.2017018

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Abstract

We present the Wigner-Lohe model for quantum synchronization which can be derived from the Schrödinger-Lohe model using the Wigner formalism. For identical one-body potentials, we provide a priori sufficient framework leading the complete synchronization, in which L²-distances between all wave functions tend to zero asymptotically.

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