Deterministic chaos in spatially homogeneous model of Abelian-Higgs theory

The chaotic properties in the Abelian-Higgs theory are numerically studied in the limit of spatially homogeneous fields. Based upon the analyses on the distribution of the Lyapunov characteristic exponents, we find that this dynamical system shows the transition from order to chaos within a certain range of the coupling constant and energy, whose property is different from the order-to-chaos transition found in the topological solutions of the SU(2) Yang-Mills-Higgs theories. It is also pointed out that the onset of chaos can be analytically described by the instability argument of the dynamical systems.