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Chaos in Yang-Mills matrix models

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2019
Başkan, Kağa
In this thesis, chaotic dynamics emerging from Yang-Mills matrix models are investigated. Firstly, we investigate the Yang-Mills two-matrix models with ChernSimons term using both analytical and numerical methods. In particular, we obtain the Poincaré sections and Lyapunov exponents at several different values of the parameters of the model, revealing the detailed structure of the chaotic dynamics. In the second part of the thesis, we focus on a massive deformation of the bosonic part of the Banks-Fischler-Shenker-Susskind (BFSS) matrix model. Using an ansatz involving fuzzy-2 and fuzzy-4 sphere configurations we determine reduced effective Hamiltonians through which we study the emerging chaotic dynamics.