The statistical description of a one-dimensional superdiffusive Lévy flier restricted to a finite domain is well known to be technically involving. For example, in this type of process the probability distribution P ( x , t ) and survival probability S ( t ) cannot be obtained from the method of images. Other methods, such as the fractional derivative approach, also find technical difficulties due to the long jumps combined with the presence of absorbing boundaries. Here we revisit this problem through a different point of view. We map the corresponding master equation to a Schrödinger-like equation and then describe the Lévy flier evolution in a Fock space. The system states are assigned to the available positions in the discrete space. The Hamiltonian-like matrix is calculated for any Lévy index α ∈ (0, 2]. For the system sizes studied here the computation of its eigenvalues and eigenvectors are performed using a symbolic computing software. ...

中文翻译：

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重新探究有界域上的Lévy航班：Fock空间方法

众所周知，一维限于限制域的一维超扩散Lévy传单的统计描述涉及到技术上。例如，在这种类型的过程中，不能从图像方法获得概率分布P（x，t）和生存概率S（t）。其他方法，例如分数导数法，由于跳远和吸收边界的存在，也发现了技术难题。在这里，我们从不同的角度重新审视这个问题。我们将相应的主方程映射到类似Schrödinger的方程，然后描述Fock空间中Lévy传单的演化。系统状态分配给离散空间中的可用位置。对于任何Lévy指数α∈（0，2]，都计算出类似哈密顿的矩阵。对于此处研究的系统大小，使用符号计算软件执行其特征值和特征向量的计算。...