We investigate the quench dynamics of a one-dimensional strongly chaotic lattice with $L$ interacting spins. By analyzing both the classical and quantum dynamics, we identify and elucidate the two mechanisms of the relaxation process of this systems: one arises from linear parametric instability and the other from nonlinearity. We demonstrate that the relaxation of the single-particles energies (global quantity) and of the onsite magnetization (local observable) is primarily due to the first mechanism, referred to as linear chaos. Our analytical findings indicate that both quantities, in the classical and quantum domain, relax at the same timescale, which is independent of the system size. The physical explanation for this behavior lies in the fact that each spin is constrained to the surface of a three-dimensional unit sphere, instead of filling the whole many-dimensional phase space. We argue that observables with a well-defined classical limit should conform to this picture and exhibit a finite relaxation time in the thermodynamic limit. In contrast, the evolution of the participation ratio, which measures how the initial state spreads in the many-body Hilbert space and has no classical limit, indicates absence of relaxation in the thermodynamic limit.
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