论文标题
量子库仑系统的动量分布的缩放行为在限制电势中
Scaling behavior of the momentum distribution of a quantum Coulomb system in a confining potential
论文作者
论文摘要
我们计算存在库仑相互作用的量子多粒子系统的单粒子动量分布和狭窄的电势。中间动量区域（限制电势）占主导地位，标志着从高速度分布有效的跨界分布到在高动量时有效的幂律行为。我们表明，对于所有动量，动量分布可以通过$ q $ -Gaussian分布来参数，其参数由限制电势指定。此外，我们发现，在比率$ q^2/ν_n$的缩放下，限制基态和$ n^{th} $兴奋状态之间过渡概率的功能形式是不变的，其中$ q $是转移的动量，$ν_n$是相应的激发能量。使用缩放变量$ q^2/ν_n$，也可以用$ q $ -Gaussian表示过渡概率的最大值。
We calculate the single-particle momentum distribution of a quantum many-particle system in the presence of the Coulomb interaction and a confining potential. The region of intermediate momenta, where the confining potential dominates, marks a crossover from a Gaussian distribution valid at low momenta to a power-law behavior valid at high momenta. We show that for all momenta the momentum distribution can be parametrized by a $q$-Gaussian distribution whose parameters are specified by the confining potential. Furthermore, we find that the functional form of the probability of transitions between the confined ground state and the $n^{th}$ excited state is invariant under scaling of the ratio $Q^2/ν_n$, where $Q$ is the transferred momentum and $ν_n$ is the corresponding excitation energy. Using the scaling variable $Q^2/ν_n$ the maxima of the transition probabilities can also be expressed in terms of a $q$-Gaussian.
