论文标题
具有单一加上随机$ k $的多屈光度量子系统的热化 - 体互动
Thermalization in many-fermion quantum systems with one- plus random $k$-body interactions
论文作者
论文摘要
我们研究了有限的多屈光度系统中具有随机$ k $ - 体相互作用的在均值场上的机制。 $ n $ n $单粒子状态的$ m $ h $的系统hamiltonian $ h $具有$ k $ - 体相互作用的单个粒子状态，由平均字段一体$ h（1）$和随机$ k $ - 体相互作用$ v（k）$具有强度$λ$。在最近将$ q $ - 赫尔米特多项式应用于这些合奏之后，对参数$ q $的完整分析描述描述了状态密度从高斯（Gaussian）的形状变化，以$ q = 1 $ $ q = 1 $ to $ q = 0 $，并以$ 0 <q <q <q <q <1 $ $ q = 0 $，以及在强度功能的差异中获得了模型模型参数。后者给出了定义热力学区域的热量标记$λ_T$。对于$λ\geλ_t$，强度函数的平滑部分由有条件的$ q $ - 正常分布（$ f_ {cn} $）很好地表示，它描述了从高斯到半圆的强度函数的过渡为$ k $ - $ k $ - 体相互作用，从$ k = 2 $ k = 2 $ m $ in $ h $ h $ h $ h $ h $。在热力学区域中，发现强度函数的前四个矩和反向参与比（IPR）的整体平均结果与相应的平滑形式非常吻合。对于较高体型的相互作用$ K $，系统可以更快地热量。
We study the mechanism of thermalization in finite many-fermion systems with random $k$-body interactions in presence of a mean-field. The system Hamiltonian $H$, for $m$ fermions in $N$ single particle states with $k$-body interactions, is modeled by mean field one-body $h(1)$ and a random $k$-body interaction $V(k)$ with strength $λ$. Following the recent application of $q$-Hermite polynomials to these ensembles, a complete analytical description of parameter $q$, which describes the change in the shape of state density from Gaussian for $q=1$ to semi-circle for $q=0$ and intermediate for $0<q<1$, and variance of the strength function are obtained in terms of model parameters. The latter gives the thermalization marker $λ_t$ defining the thermodynamic region. For $λ\ge λ_t$, the smooth part of the strength functions is very well represented by conditional $q$-normal distribution ($f_{CN}$), which describes the transition in strength functions from Gaussian to semi-circle as the $k$-body interaction changes from $k = 2$ to $m$ in $H$. In the thermodynamic region, ensemble averaged results for the first four moments of the strength functions and inverse participation ratio (IPR) are found to be in good agreement with the corresponding smooth forms. For higher body rank of interaction $k$, system thermalizes faster.
