The Lyapunov Exponents of Thirring Instantons

Recently, nonlinear differential equations corresponding to pure spinor instanton solutions were obtained by using Heisenberg anzat in the 2D Thirring Model, which has been used as a toy model in Quantum field theory. In addition, the evolution of spinor type instanton solutions in phase space was investigated according to the change in the constant parameter β. Spinor instanton dynamics is a special case in which nonlinear terms play an important role. Chaos describes certain nonlinear dynamical systems that depend very precisely on initial conditions. Lyapunov exponents are an important method for measuring stability and deterministic chaos in dynamical systems. Lyapunov exponents characterize and quantify the dynamics of small perturbations of a state or orbit in state space. In this study, Lyapunov spectrum of spinor type instanton solutions was investigated by examining the largest local and global Lyapunov exponents. As a result of the Lyapunov Spectrum, it was determined that the spinor type instanton solutions exhibit chaotic behavior at parameter value β = 2. Periodic and quasi periodic behaviors were detected when the parameter values were β < 2. In cases of β > 2, weak chaotic behaviors were observed. This study demonstrates that Thirring Instantons, which are spinor type instanton solutions, exhibit chaotic properties.

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