本文以混合表象來表示電子－原子核之全量子系統，對於電子部份，可得到與Schrdinger表象類似的形式，以習慣的波函數來描述電子運動，對於原子核部份，則可得到與Heisenberg表象類似的形式，以類比於古典力學的運動方程式來描述原子核運動；混合表象可用於量子統計力學，且方便用於量子－古典混合系統的推導。本文並證明正則系綜下等溫處理的分子動力學應配合正則系綜時依密度泛函理論，而非文獻中配合微正則系綜之時依密度泛函理論。最後針對不同溫度、不同晶軸方向下金奈米線於高應變率拉伸下的力學行為做廣泛地分析，探討其應力分佈、截面積變化、徑向分布函數的演化與分布、應力、能量與應變關係圖與最大應力、Young係數等性質，並以共同鄰近粒子分析法分析其局部結構變化，發現其應力與能量的轉折與局部結構變化有密切關係，最大應力與Young係數與應變率也有關聯存在。根據這些平滑變化的局部結構與機械性質，我們進而預測高應變率下電導量子化情形不會出現。

　The mixed picture is introduced to represent electronic-nucli quantum system. The Schrdinger-like equations can be obtained for electrons, and the wave function can be habitually used for the motion of electrons. On the other hand, the Heisenberg-like equations of motion can be obtained for nuclei and are analogous to classical mechanics. The mixed picture can be applied to the quantum statistical mechanics and can be conveniently used to derive the equations of motion of the mixed quantum-classical system. The proof is also derived that under canonical ensemble, the isothermal molecular dynamics should be combined with the canonical time-dependent density-functional theory instead of microcanonical one which was used by a reference. The effects of high strain-rate on mechanical behavior of gold nanowire are studied under different temperatures and different crystalline orientations. The properties are focused such as the distributions of stresses, the changes of cross sections, the evolutions and distributions of radial distribution functions, stress-strain and energy-strain relations, maximum strengths, and Young’s moduli. The common neighbor analysis is used to study the changes of local structures and the corresponding relations to stresses and energies. The maximum strengths and Young's moduli are also related to strain-rates. According to the smooth changes of local structures and mechanical properties, we predict that the quantized conductivities, which occur under lower strain-rate, will not be observed under high strain-rate.

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