Wavelet imaging of transient energy localization in nonlinear systems at thermal equilibrium: The case study of NaI crystals at high temperature

In this paper we introduce a method to resolve transient excitations in time-frequency space from molecular dynamics simulations. Our technique is based on continuous wavelet transform of velocity time series coupled to a threshold-dependent filtering procedure to isolate excitation events from background noise in a given spectral region. By following in time the center of mass of the reference frequency interval, the data can be easily exploited to investigate the statistics of the burst excitation dynamics, by computing, for instance, the distribution of the burst lifetimes, excitation times, amplitudes and energies. As an illustration of our method, we investigate transient excitations in the gap of NaI crystals at thermal equilibrium at different temperatures. Our results reveal complex ensembles of transient nonlinear bursts in the gap, whose lifetime and excitation rate increase with temperature. The method described in this paper is a powerful tool to investigate transient excitations in many-body systems at thermal equilibrium. Our procedure gives access to both the equilibrium and the kinetics of transient excitation processes, allowing one in principle to reconstruct the full picture of the dynamical process under examination.