The Lyapunov Exponents of Thirring Instantons

Abstract

Recently, nonlinear differential equations corresponding to pure spinor instanton solutions have been obtained by using Heisenberg ansatz in the 2D Thirring Model, which is used as a subject 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, The chaotic behavior of spinor type instanton solutions is analyzed by numerical study of the time evolution of the Lyapunov exponents. Moreover, the Lyapunov spectrum of spinor type instanton solutions with respect to varying the parameter are plotted. 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.