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Title Finite-size effects in Kuramoto type systems from Large Deviation perspective
Speaker Rupak Majumder (Tata Institute of Fundamental Research, Mumbai)
Date&time 📅 Wednesday, April 16
🕓 14.00 (Rome) (ATTENTION: Not usual day and time!!)
Location room 138 (SISSA, via Bonomea)
Abstract Synchronization is observed in a variety of physical systems, from electrical networks to flocking birds. These complex systems are typically described at the microscopic level by a large number N of interacting basic units. A common approach to studying such systems is to take the infinite-N limit and analyze the one-particle distribution function. However, when N is large but finite, these calculations are no longer strictly valid, and it becomes crucial to properly account for finite-N fluctuations. The study of these fluctuations has been largely numerical. From a theoretical perspective, while finite-N fluctuations due to quenched disorder have been studied for few specific cases, the effects of finite-N fluctuations arising from annealed disorder remain largely unexplored. In this work, we analyze a system with both quenched and annealed disorder and systematically reduce the large-deviation principle (LDP) for the one-particle distribution function to an LDP for the macroscopic order parameter. For a variety of models, both equilibrium and non-equilibrium, we observe that the time evolution of the order parameter for a finite-N system follows a Brownian motion in an effective two-dimensional potential, with the Brownian noise vanishing in the infinite-N limit. We compare our theoretical results with direct numerical simulations and find excellent agreement.
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