论文标题
谐波链中的量子与热波动和实验意义
Quantum versus thermal fluctuations in the harmonic chain and experimental implications
论文作者
论文摘要
量子机械谐波振荡器的非零地面能意味着电势的最小量子波动，均值与普朗克常数成正比的均值值。在经典力学中，当振荡器耦合到温度$ t $的热浴时，热波动发生。在有限温度下，量子统计力学可以描述从$ t = 0 $的纯量子波动到高温极限下的经典热波动的过渡。 PEIERL早期指出，{\ it和谐波链}中的均方根热波动与链中原子的距离增加了{\ it线性}，从而破坏了远距离结晶顺序。相应的纯量子波动导致较慢的{\ it对数}随着链条固定端的距离而增加。还表明，这意味着，例如，在零温度下，在无限链中X射线散射中没有尖峰的峰值，而相反，它显示了一维量子液体典型的功率定律行为（称为{\ IT luttinger液体}）。
The nonzero ground-state energy of the quantum mechanical harmonic oscillator implies quantum fluctuations around the minimum of the potential with the mean square value proportional to Planck's constant. In classical mechanics thermal fluctuations occur when the oscillator is coupled to a heat bath of temperature $T$. At finite temperature quantum statistical mechanics allows the description of the transition from pure quantum fluctuations at $T=0$ to classical thermal fluctuations in the high temperature limit. It was early pointed out by Peierls that the mean square thermal fluctuations in a {\it harmonic chain} increase {\it linearly} with the distance of the atoms in the chain, destroying long range crystalline order. The corresponding pure quantum fluctuations lead to a much slower {\it logarithmic} increase with the distance from the fixed end of the chain. It is also shown that this implies, for example, the absence of sharp Bragg peaks in x-ray scattering in an infinite chain at zero temperature, which instead show power law behaviour typical for one dimensional quantum liquids (called {\it Luttinger liquids}).
