Coherence measure in Hamiltonian systems with many degrees of freedom

We study the phase space region of two- and three-dimensional lattices where a transition from chaotic to ordered dynamics takes place when the energy is lowered. In this region we find coexistence of degrees of freedom (DOF’s), endowed with different levels of chaos. The analysis of this complex dynamical pattern requires the introduction of diagnostic tools suitable for a characterization of single DOF’s: coherence angles and coherence times. We find that the coherence times—which give a measure of the time each DOF needs to relax to equilibrium—are roughly proportional to the inverse of the specific energy. This may be useful to evaluate the reliability of statistical results obtained in computer experiments performed on condensed matter systems at low energy.