JournalsemssVol. 3 , No. 2pp. 209–267

Collective synchronization of classical and quantum oscillators

  • Seung-Yeal Ha

    Seoul National University, South Korea
  • Dongnam Ko

    Seoul National University, South Korea
  • Jinyeong Park

    Universidad de Granada, Spain
  • Xiongtao Zhang

    Seoul National University, South Korea
Collective synchronization of classical and quantum oscillators cover
Download PDF

A subscription is required to access this article.

Abstract

Synchronization of weakly coupled oscillators is ubiquitous in biological and chemical complex systems. Recently, research on collective dynamics of many-body systems has been received much attention due to their possible applications in engineering. In this survey paper, we mainly focus on the large-time dynamics of several synchronization models and review state-of-art results on the collective behaviors for synchronization models. Following a chronological order, we begin our discussion with two classical phase models (Winfree and Kuramoto models), and two quantum synchronization models (Lohe and Schrödinger–Lohe models). For these models, we present several sufficient conditions for the emergence of synchronization using mathematical tools from dynamical systems theory, kinetic theory and partial differential equations in a unified framework.

Cite this article

Seung-Yeal Ha, Dongnam Ko, Jinyeong Park, Xiongtao Zhang, Collective synchronization of classical and quantum oscillators. EMS Surv. Math. Sci. 3 (2016), no. 2 pp. 209–267

DOI 10.4171/EMSS/17