论文标题
tsallis分布，放松和关系$Δt\cdotΔe\ simeq h $，在经典模型的动态波动中
Tsallis distributions, their relaxations and the relation $Δt \cdot ΔE \simeq h$, in the dynamical fluctuations of a classical model of a crystal
论文作者
论文摘要
我们报告了在动力学系统理论框架中进行的数值研究的结果，这是一个离子晶体的现实模型，由于存在长距离库仑相互作用，吉布斯分布没有很好地定义。使用Maxwell-Boltzmann分布的初始数据，用于模式 - e_k $，我们研究动态波动，计算能量变化的模量$ | e_k（t）-e_k（0）| $。主要的结果是他们遵循Tsallis分布，这些分布在接近Maxwell Boltzmann的分布中放松。还指出该系统保持相关。放松时间$τ$取决于特定的能量$ \ varepsilon $，对于曲线$τ$ vs，$ \ varepsilon $一个一个结果有两个结果。首先，存在一个能量阈值$ \ VAREPSILON_0 $，曲线具有$$的表格 τ\ cdot \ varepsilon \ simeq h \，$$，出乎意料的是，普朗克的常数$ h $出现。就模式能量的标准偏差$ΔE$而言（其中一个具有$δe= \ Varepsilon $），用$ΔT$表示放松时间$τ$，该关系读取$Δt\cdotΔee\ simeq H $，这使Heisenberg Incnationtity Interation Timentity Interation Tirantation the Heisenberg Interation Tirantation to。此外，阈值对应于零点能。实际上，后者的量子值为$hν/2 $（其中$ν$是系统的特征频率），而我们发现$ \ varepsilon \ simeqhν/4 $，因此只有一个因子差异为2。
We report the results of a numerical investigation, performed in the frame of dynamical systems' theory, for a realistic model of a ionic crystal for which, due to the presence of long--range Coulomb interactions, the Gibbs distribution is not well defined. Taking initial data with a Maxwell-Boltzmann distribution for the mode-energies $E_k$, we study the dynamical fluctuations, computing the moduli of the the energy-changes $|E_k(t)-E_k(0)|$. The main result is that they follow Tsallis distributions, which relax to distributions close to Maxwell-Boltzmann ones; indications are also given that the system remains correlated. The relaxation time $τ$ depends on specific energy $\varepsilon$, and for the curve $τ$ vs, $\varepsilon$ one has two results. First, there exists an energy threshold $\varepsilon_0$, above which the curve has the form $$ τ\cdot \varepsilon \simeq h\ , $$ where, unexpectedly, Planck's constant $h$ shows up. In terms of the standard deviation $ΔE$ of a mode-energy (for which one has $ΔE=\varepsilon$), denoting by $Δt$ the relaxation time $τ$, the relation reads $Δt \cdot ΔE \simeq h$, which reminds of the Heisenberg uncertainty relation. Moreover, the threshold corresponds to zero-point energy. Indeed, the quantum value of the latter is $hν/2$ ( where $ν$ is the characterisic infrared frequency of the system), while we find $\varepsilon \simeq hν/4$, so that one only has a discrepancy of a factor 2. So it seems that lack of full chaoticity manifests itself, in Statistical Thermodynamics, through quantum-like phenomena.
