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Center for Nonlinear Studies |
A sound notion of integrability for quantum systems has remained elusive for decades. As a result, conditions for e.g. the absence of thermalization, Poisson level statistics, and level crossings in integrable Hamiltonians are similarly vague. This is particularly relevant nowadays when dynamical and equilibrium properties of many integrable systems became experimentally accessible. In this talk, I will propose a surprisingly simple and yet unambiguous notion of quantum integrability leading to specific results, such as new integrable models, ensemble theory of quantum integrability (Integrable Matrix Theory, cf. Random Matrix Theory for chaotic systems) and precise criteria for Poisson statistics and level crossings. I will also explain in simple terms and prove the Generalized Gibbs Ensemble for nonlinear integrable dynamics.
Host: Nikolai Sinitsyn