Lennard-Jones流體之瞬間正則模頻譜內遷移邊界隨作用力範圍,溫度及密度之變化

Abstract

在瞬間正則模頻譜中，分別在實頻與虛頻瞬間正則模頻譜上發現遷移邊界。由於計算上的難度，在本文中只有探討虛頻之遷移邊界。我們對瞬間正則模做多重碎形的分析。在遷移邊界附近，瞬間正則模會表現出多重碎形的特性。我們計算五個不同尺寸的系統之奇異力，利用奇異力在遷移邊界附近不會隨系統大小而改變的特性，在分析數據的誤差範圍內，求得其遷移邊界的位置。然後再依序改變交互作用力範圍，及流體的熱力學狀態，在溫度或密度的改變下，探討系統在快進入玻璃態時，遷移邊界位置的轉變。 從我們的數據可得，當增加吸引力或增加密度時，局域瞬間正則模之比例會隨之減少。而降低溫度時，也會使局域瞬間正則模之比例減少。未來還可以探討系統在玻璃態，遷移邊界位置的變化。

Two mobility edges (MEs) are found in the instantaneous normal mode (INM) spectrum of a simple fluid, with one in the real-frequency branch and the other in the imaginary-frequency branch. Due to the complexity in calculations for the real-frequency ME, we only investigate the ME in the imaginary-frequency branch in this thesis. In terms of the multifractal analysis, the INM eigenvectors near a ME exhibit a multifractal nature with universal generalized fractal dimensions and the singularity spectrum. We calculate the singularity strengths of a Lennard-Jones (LJ) fluid for five system sizes. With the property that the singularity strengths near a ME reveal the system-size invariance, within numerical errors, we obtain the location of the ME in the imaginary-frequency branch of a LJ fluid. By changing the interaction range of the LJ fluid and different thermodynamic states in turn, we investigate the variation of the ME location with the temperature or density of the LJ fluid close to a glassy state and the variation with the interaction range of the LJ potential. According to our results, with the attractive force or by increasing the fluid density, the ratio of the imaginary-frequency localized INMs decreases. As the fluid temperature decreases, the ratio of the imaginary-frequency localized INMs also decreases. For the future works, the variations of the MEs in the glassy systems are worthy investigating.