论文标题
在特定边界条件下具有不对称远距离跳跃的非铁链的精确溶液
Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions
论文作者
论文摘要
我们研究了具有不对称的长距离跳跃并探索以在某些特定边界条件下解决系统的一维通用非热模型。尽管引入远程跳跃术语使我们无法找到任意边界参数的分析解决方案，但是当边界参数满足某些约束关系时，我们确定了精确解决方案的存在，从而赋予特定的边界条件。我们的分析结果表明，波函数采用简单的形式，并且独立于跳跃范围，而特征值光谱显示丰富的模型依赖性结构。特别是，我们发现存在特殊点是伪周期性边界条件的存在，当跳跃参数满足某些条件时，特征值与周期系统相同，而特征态则表现出非富甲虫的皮肤效应。
We study one-dimensional general non-Hermitian models with asymmetric long-range hopping and explore to analytically solve the systems under some specific boundary conditions. Although the introduction of long-range hopping terms prevents us from finding analytical solutions for arbitrary boundary parameters, we identify the existence of exact solutions when the boundary parameters fulfill some constraint relations, which give the specific boundary conditions. Our analytical results show that the wave functions take simple forms and are independent of hopping range, while the eigenvalue spectra display rich model-dependent structures. Particularly, we find the existence of a special point coined as pseudo-periodic boundary condition, for which the eigenvalues are the same as the periodical system when the hopping parameters fulfill certain conditions, whereas eigenstates display non-Hermitian skin effect.
