https://polytechnique.hal.science/hal-01875206Golse, FrançoisFrançoisGolseCMLS - Centre de Mathématiques Laurent Schwartz - X - École polytechnique - CNRS - Centre National de la Recherche ScientifiqueHa, Seung-YealSeung-YealHaSNU - Seoul National University [Seoul]KIAS Séoul - School of Mathematics - KIAS - Korea Institute for Advanced StudyA MEAN-FIELD LIMIT OF THE LOHE MATRIX MODEL AND EMERGENT DYNAMICSHAL CCSD2018BBGKY hierarchyKuramoto modelLohe modelMean-field limitQuantum synchronization[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]Golse, François2018-09-17 10:12:482023-03-24 14:53:082018-09-20 13:26:04enPreprints, Working Papers, ...application/pdf1The 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.