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Explore the formation and behavior of polariton condensates in axially symmetric traps with weak rotating potentials in this 40-minute conference talk. Delve into direct numerical simulations of the two-dimensional Gross-Pitaevskii equation, revealing how potential rotation influences condensate spin. Discover the intriguing phenomenon where the direction of polariton flow can depend on the angular velocity of the potential, sometimes aligning with or opposing the rotation direction. Examine the development of a coupled mode theory explaining the "winner takes all" scenario near the condensation threshold, where the fastest-growing linear mode determines the condensate's final state. Investigate the challenges of realizing this dynamics in vector cases with incoherent pump excitation of both circular polarizations. Gain insights into 2D numerical simulations and perturbation theory demonstrating how vector cases can lead to simultaneous excitation of different modes, resulting in polariton condensates with time-periodic polarization oscillations.
