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

Abstract

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 manybody 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.

Mechanisms for transient localization in a diatomic nonlinear chain

“…n summing the corresponding equations for first and second order. To obtain the dissipation term as in (16), in (31) we make the replacement d dT dA n dT ≈ iΩ 0 dA n dT which is justified within the slowly-variable amplitude hypotesis. The simplified equations ( 16) are obtained neglecting U…”

“…A convenient way to analyze non-stationary signals is to use a wavelet analysis in the time-frequency domain. This technique proved to be useful to pinpoint transient vibrational excitations in many-body system starting from simple chain models [13] to simulated NaI crystals [31]. This method allows to detect transient frequency components appearing at specific times and lasting for finite lapses of time.…”

Prediction and observation of intermodulation sidebands from anharmonic phonons in NaBr

“…Exceptions are predictions [6,7] and experimental reports of intrinsic localized modes (ILMs) [8][9][10][11][12]. There are different viewpoints about the experimental evidence for ILMs, however [13][14][15].…”

Effect of discrete breathers on the specific heat of a nonlinear chain

“…For the first time, this method was successfully applied to the study of gap DBs in alkali halide NaI crystal [38] and this study was continued in refs. [39,40]. Using molecular dynamics, DBs have been found in monoatomic Morse crystals [41,42], covalent crystals Si, Ge and diamond [43,44], pure metals [45][46][47][48][49][50], ordered alloys [51][52][53][54], carbon and hydrocarbon nanomaterials [55][56][57][58][59][60][61][62][63][64][65][66][67], boron nitride [68], and proteins [69][70][71][72].…”

“…Identification of thermally excited DBs in lattices requires application of special procedures [40,74,[76][77][78][79][80][81]. DBs, as lattice defects, can be distinguished in lattice during the non-equilibrium processes e.g.…”