We have studied correlational properties of quasi-one-dimensional electron gas at finite temperature $T$ by incorporating the dynamics of electron correlations within the quantum version of the self-consistent mean-field approach of Singwi, Tosi, Land, and Sj\"{o}lander. Static structure factor, pair-correlation function, static density susceptibility, excess kinetic energy, and free correlation energy are calculated covering a wide range of temperature and electron number density. As at absolute zero temperature, the inclusion of dynamics of correlations results in stronger spatial electron correlations, with a pronounced peak in the static structure factor at wave vector $q\sim 3.5 k_F$, which grows further with decreasing electron density. Below a critical density, the static density susceptibility seems to diverge at this value of $q$, signaling a transition from liquid to the Wigner crystal state- a prediction in qualitative agreement with recent simulations and experiment. However, thermal effects tend to impede crystallization with the consequence that the critical density decreases significantly with rising $T$. On the other hand, the pair-correlation function at short range exhibits a non-monotonic dependence on $T$, initially becoming somewhat stronger with rising $T$ and then weakening continuously above a sufficiently high $T$. The calculated free correlation energy shows a noticeable dependence on $T$, with its magnitude increasing with increase in $T$. Further, we have looked into the effect of temperature on the frequency-dependence of dynamic local-field correction factor and the plasmon dispersion. It is found that with rising $T$ the dynamics of correlations weakens, and the plasmon frequency exhibits a blue shift. Wherever interesting, we have compared our results with the lower-order approximate calculations and zero-$T$ quantum Monte Carlo simulations.

中文翻译：

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动态相关效应对有限温度准一维电子气相关特性的影响


我们通过将电子相关动力学纳入 Singwi、Tosi、Land 和 Sj 自洽平均场方法的量子版本中，研究了有限温度 $T$ 下准一维电子气的相关特性\" {o}lander。计算了静态结构因子、对相关函数、静态密度磁化率、过剩动能和自由相关能，涵盖了广泛的温度和电子数密度，在绝对零温度下，包含了动力学。相关性导致更强的空间电子相关性，静态结构因子在波矢 $q\sim 3.5 k_F$ 处有一个明显的峰值，随着电子密度的降低而进一步增长，低于临界密度，静态密度磁化率似乎在此发散。 $q$ 的值，标志着从液体到维格纳晶体状态的转变 - 与最近的模拟和实验定性一致的预测然而，热效应往往会阻碍结晶，结果是临界密度随着 $T$ 的增加而显着降低。 。另一方面，短程的配对相关函数表现出对 $T$ 的非单调依赖性，最初随着 $T$ 的上升而变得有些强，然后在足够高的 $T$ 之上持续减弱。计算出的自由相关能显示出对 $T$ 的明显依赖性，其幅度随着 $T$ 的增加而增加。此外，我们还研究了温度对动态局部场校正因子和等离子体色散的频率依赖性的影响。研究发现，随着$T$的增加，相关性的动态减弱，等离子体激元频率呈现蓝移。 只要有趣，我们就将我们的结果与低阶近似计算和零 $T$ 量子蒙特卡罗模拟进行比较。