A MEAN-FIELD LIMIT OF THE LOHE MATRIX MODEL AND EMERGENT DYNAMICS

François Golse (1) , Seung-Yeal Ha (2, 3)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 SNU - Seoul National University [Seoul]
3 KIAS Séoul - School of Mathematics

The Lohe matrix model is a continuous-time dynamical system describing the collective dynamics of group elements in the unitary group man-ifold, and it has been introduced as a toy model of a non abelian generalization of the Kuramoto phase model. In the absence of couplings, it reduces to the finite-dimensional decoupled free Schrödinger equations with constant Hamiltonians. In this paper, we study a rigorous mean-field limit of the Lohe matrix model which results in a Vlasov type equation for the probability density function on the corresponding phase space. We also provide two different settings for the emergent synchronous dynamics of the kinetic Lohe equation in terms of the initial data and the coupling strength.

Mots clés: BBGKY hierarchy; Kuramoto model; Lohe model; Mean-field limit; Quantum synchronization

Domaines: Systèmes dynamiques [math.DS]; Equations aux dérivées partielles [math.AP]

François Golse, Seung-Yeal Ha. A MEAN-FIELD LIMIT OF THE LOHE MATRIX MODEL AND EMERGENT DYNAMICS. 2018. ⟨hal-01875206⟩