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

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

doi:10.3934/nhm.2017018

Article Contents

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: February 2017

Revised: June 2017

Published: October 2017

The work of P. Antonelli and P. Marcati is partially supported by PRIN grant 2015YCJY3A 003 and by G.N.A.M.P.A. (I.N.d.A.M.), The work of S.-Y. Ha and D. Kim are partially supported by the National Research Foundation of Korea (NRF2017R1A2B2001864).

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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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Mathematics Subject Classification: Primary: 35Q40; Secondary: 82C22, 93D20, 35B40.

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