主讲人：Matteo Colangeli（拉奎拉大学）

题目：Exact Response Theory and Kuramoto Dynamics

时间：2023年10月12日上午09:00

地点：理工楼1226

报告摘要：

The study of collective behavior in systems with many degrees of freedom is part of a large interdisciplinary research effffort, which involves e.g. mathematicians, physicists, biologists and engineers. The Kuramoto model deserves a special mention in this fifield, as it constitutes an exactly solvable model which gives rise to synchronization, a phenomenon that appears to be ubiquitous in Nature. In our work we address the analysis of the foregoing model through the prism of statistical mechanics, in which some known mathematical results can be reinterpreted in a new light. The dynamics of Kuramoto oscillators is investigated via the exact response theory based on the Dissipation Function, which has been introduced in the fifield of nonequilibrium molecular dynamics. We recall that while Linear Response Theory is a milestone of nonequilibrium statistical mechanics, it does not apply, in general, to systems undergoing phase transitions. The Kuramoto dynamics is thus studied analytically and numerically as a testbed for the exact theory mentioned above. We succeed to derive explicit formulae for the two-time correlation functions and for the asymptotic value of the Dissipation Function. Remarkably, we highlight the non-monotonic behavior of the correlations as functions of time, when the number of oscillators becomes large. We also compare our results with the predictions of the classical Linear Response Theory. Our analysis reveals that the exact response formalism, at variance with classical Kubo’s theory, can properly detect the phase transition, characterized by a phase synchronization of the oscillators.

个人简介：

Matteo Colangeli, Associate Professor of Mathematical Physics at the University of L’Aquila (Italy). He pursued his Ph.D. at ETH Zurich (Switzerland), where he defended a thesis focusing on the derivation of hydrodynamics from the Boltzmann equation in the

rarefified regime of moderate Knudsen numbers. After completing his doctoral program (July 2009), he did a postdoc at the School of Mathematical Sciences of Queen Mary University of London (U.K.), where he did research on the theory of flfluctuation relations for dissipative chaotic dynamical systems. Then, he did a postdoc at the Polytechnic University of Turin (Italy), where he focused on quantum disordered systems as well as on artifificial neural networks through the prism of statistical mechanics. In November 2016 he started working as a lecturer at the University of L’Aquila. Last, he research interests mostly focus on the study of models of nonequilibrium statistical mechanics, by alternating rigorous calculations with Monte Carlo simulations.