Simulations for the time evolution of instantaneous resonant modes: Creation, annihilation and mode exchange

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Abstract

In this paper, we simulate the time evolution of the instantaneous resonant modes (IRMs), which are quasilocalized, in a model of Ga liquid. Through the simulations, we have observed the whole process from creation to annihilation of each individual IRM, and its lifetime is, therefore, estimated. We also find the exchange in character between an IRM and a non-resonant instantaneous normal mode (INM). The exchange occurs as the two INMs have very close frequencies and share a common central particle.

Introduction

Resonant modes, the low-frequency quasilocalized vibrational excitations, play an important role on the low-temperature properties of glassy materials [1]; however, the microscopic features of the resonant modes are not fully understood [2]. Especially, how the resonant modes are created and annihilated and how they evolve in time are still open questions. Computer simulation is available for studying these problems; however, it takes a quite long computing time for the glassy systems.

Down to the single-particle regime, the short-time liquid dynamics can be exactly described by the instantaneous-normal-mode (INM) approach [3], [4], in which the potential energy surface near each configuration is approximated by a harmonic one with the same curvatures. Becuause the anharmonicity of the extraordinarily rugged potential energy landscape of a liquid, the INMs lose their identities via either adiabatically evolving to new INMs of configuration at the next instant or temporarily destructed by mixing two INMs as their frequencies get very close [5]. Thus, each individual INM actually survives for a short lifetime, but with some created and some destroyed during time evolution, the overall INM density of state (DOS) of a liquid, after averaged over configurations, keeps stable.

Encouraged by the recent investigations in terms of inelastic X-ray scattering techniques, the study of microscopic dynamics in liquid metals is continuously an interesting topic [6]. Recently, in a model of Ga liquid, the low-frequency quasilocalized INMs, termed as instantaneous resonant modes (IRMs), have been numerically evidenced [7], and the local structures around the quasilocalization center of an IRM have been reported [8]. The occurrence of the IRMs in this model is attributed to two factors: (A) the well-known curvature dip in the repulsive core of a Ga atom, with the atoms in this shell region being weakly connected in vibration with the central one, and (B) the local volume expansion, which pushes more neighbors of a Ga atom into this shell region. Due to the coorperation of the two factors, the center of a quasilocalized vibration is instantaneously created at a Ga atom, which is more weakly coupled with its neighbors than the other atoms. The energy profile along the eigenvector of an IRM can be generally described by the soft-potential model, which is typical for the resonant modes found in a glassy system [9], [10]. Thus, the IRMs are quite similar in feature as the resonant modes in glassy systems, except for short lifetimes. In this paper, we will study the time evolution of the IRMs in the Ga-liquid model through tracing the INMs with computer simulation.

Section snippets

The simulation

We have performed MD simulations of 500 Ga particles in equilibrium liquid states at pressure about 1 bar; the details of the Ga pseudopotential and our simulations are referred to Ref. [11]. Our model has an accurate fit for the experimental structure factors of Ga liquid. The velocity autocorrelation function Cv(t) at T = 973 K obtained from our MD simulations and its power spectrum are presented in Fig. 1. The INM and IRM DOS of our model have been given in Ref. [7]. Shown in Fig. 1 is also

Results

The time evolution of several INMs in a low-frequency window in the real branch is presented in Fig. 2, in which only the numerical data are shown and there are no continuous lines connecting any two data points at succesive time steps. Because of the small time step, the trajectories of these INM frequencies are generally catched, and the modulation of a trajectory in this low-frequency region varies gently. However, due to the discreteness of the data points, it is hard to tell whether two

Conclusion

In this paper, the time evolution of the IRMs, from creation to annihilation, in a model of Ga liquid has been simulated. Through the simulations, the lifetimes of the IRMs are estimated to be of fs order. We also present the numerical evidence for the exchange in character between a IRM and an INM extended in space; this occurs as the two INMs are close in frequency and share a common central particle. This mode exchange is considered as a mechanism to elongate the IRM lifetime.

Acknowledgements

T.M. Wu would like to acknowledge support from the National Science Council of Taiwan, R.O.C. under grant No. NSC 94-2112-M009016.

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