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Explore the analytical and numerical analysis of many-anyon quantum gas systems confined in a plane with trapping potential through this mathematical conference talk. Delve into recent collaborative research examining particles that are close to bosonic behavior, parametrized by small magnetic flux attachment and additional "spin-orbit" interaction parameters. Learn how the low-energy landscape of the emerging effective nonlinear and nonlocal Chern-Simons-Schrödinger energy functional can be explored using the concept of "nonlinear Landau levels," featuring explicit supersymmetric soliton solutions discovered by Jackiw and Pi in the early 1990s. Discover how the stability of the gas against collapse increases linearly with increasing flux due to the formation of counter-rotating vortices, providing insights into emergent phenomena in many-body quantum systems through advanced mathematical physics approaches.
