title: Synchronization in a semiclassical Kuramoto model.
abstract: Synchronization is a ubiquitous phenomenon occurring in social, biological, and technological systems when the internal rythms of their constituents are adapted to be in unison as a result of their coupling. This natural tendency towards dynamical consensus has spurred a large body of theoretical and experimental research in recent decades. The Kuramoto model constitutes the most studied and paradigmatic framework in which to study synchronization. In particular, it shows how synchronization appears as a phase transition from a dynamically disordered state at some critical value for the coupling strength between the interacting units. The critical properties of the synchronization transition of this model have been widely studied and many variants of its formulations have been considered to address different physical realizations. However, the Kuramoto model has been studied only within the domain of classical dynamics, thus neglecting its applications for the study of quantum synchronization phenomena. Based on a system-bath approach and within the Feynman path-integral formalism, we derive equations for the Kuramoto model by taking into account the first quantum fluctuations. We also analyze its critical properties, the main result being the derivation of the value for the synchronization onset. This critical coupling increases its value as quantumness increases, as a consequence of the possibility of tunneling that quantum fluctuations provide.
authors.affiliation: Departamento de Física de la Materia Condensada, Universidad de Zaragoza, E-50009 Zaragoza, Spain.
authors.forename: Ignacio
authors.initials: I
authors.lastname: Hermoso de Mendoza
authors.affiliation: Grupo de Física Atómica y Molecular, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA; Calle 70 No. 52-21, Medellín, Colombia.
authors.forename: Leonardo A
authors.initials: LA
authors.lastname: Pachón
authors.affiliation: Departamento de Física de la Materia Condensada, Universidad de Zaragoza, E-50009 Zaragoza, Spain and Instituto de Biocomputación y Física de Sistemas Complejos, Universidad de Zaragoza, E-50018 Zaragoza, Spain.
authors.forename: Jesús
authors.initials: J
authors.lastname: Gómez-Gardeñes
authors.affiliation: Departamento de Física de la Materia Condensada, Universidad de Zaragoza, E-50009 Zaragoza, Spain and Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, E-50012 Zaragoza, Spain and Fundación ARAID, Paseo María Agustín 36, E-50004 Zaragoza, Spain.
authors.forename: David
authors.initials: D
authors.lastname: Zueco