This talk will cover two distinct topics relating to dynamical systems. The phenomenon of Bose-Einstein condensation, whereby many particles spontaneously behave as a single quantum state, may be observed in part-light, part-matter particles called polaritons which occur in semiconductor microcavities. This new type of condensate is inherently out of equilibrium, and its dynamics are governed by a driven-dissipative generalization of the Gross-Pitaevskii equation. When many such condensates are localized in a lattice potential with static disorder, their dynamics may be mapped to a model of coupled phase oscillators with random natural frequencies, which is shown to undergo a phase transition from a desynchronized state to one with global frequency synchronization.
We will also discuss how more generally, the evolution of nonlinear stochastic systems may be reconstructed by studying the properties of the Koopman operator, which acts on observables of the system. By reconstructing the Koopman operator using data-driven methods, one can calculate the response of nonlinear systems to perturbation in terms of the various modes of variability of the system. This can provide a novel method of predicting the response of the climate to forcing.
Speaker’s Bio: John Moroney is a postdoctoral research associate in the Mathematics of Planet Earth research division at the University of Reading, United Kingdom. He received a Ph.D. in Physics from Trinity College Dublin in 2022, following the completion of a B.S. in Theoretical Physics at the same university in 2017. His research interests include dynamical systems, statistical mechanics, and climate dynamics.
Last Updated: March 15, 2024 - 9:39 am