hide
Free keywords:
-
Abstract:
Coupled oscillators have a wide range of applications in statistical mechanics. Often, systems under study might present several scales of description. In this case, each unit of the system might be as well composed by a finite number of oscillators. However, standard mean-field theories only deal with populations in the thermodynamic limit, which lead to deterministic solutions for the order parameters. In this talk, I will introduce a novel approach to tackle this problem, which applies to any population of oscillators subject to stochastic white noise. I will apply the theory to the stochastic Kuramoto model deriving formally the multiplicative noise emerging in the mesoscopic limit, as well as finding deterministic finite-size corrections. I will show how these results allow us to derive, for the first time, almost-exact closed solutions for the stochastic Kuramoto model, as well as new insights in the critical transition to synchrony.
