| 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. |
| 🔗 Past seminars | |
| 🔗 Past journal club meetings |
