{\cal PT} symmetry breaking and exceptional points for a class of inhomogeneous complex potentials
{\cal PT} symmetry breaking and exceptional points for a class of inhomogeneous complex potentials
复制标题
{cal PT} 一类非齐次复势的对称破缺和异常点
DOI：
10.1088/1751-8113/42/46/465302
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Dorey P
中科院分区：
文献类型：
--
作者：
Dorey P
我们研究了一个三参数家庭的对称哈密顿，通过ODE/IM对应的Perk-Schultz模型。我们表明，真实的特征值合并，并成为复杂的二次和三次例外点，并探讨相应的约旦块结构，利用准精确解的模型的一个子集。相图的映射是使用数值，分析和微扰方法的组合完成的。除其他事项外，这揭示了一些新的性质的本德-邓恩多项式，并提供了新的见解相变无限多复杂的特征值，这是第一次观察到的本德和Boettcher。一个新的精确可解极限，非齐次复方井，也被确定。
We study a three-parameter family of-symmetric Hamiltonians, related via the ODE/IM correspondence to the Perk–Schultz models. We show that real eigenvalues merge and become complex at quadratic and cubic exceptional points, and explore the corresponding Jordan block structures by exploiting the quasi-exact solvability of a subset of the models. The mapping of the phase diagram is completed using a combination of numerical, analytical and perturbative approaches. Among other things this reveals some novel properties of the Bender–Dunne polynomials, and gives new insight into a phase transition to infinitely many complex eigenvalues that was first observed by Bender and Boettcher. A new exactly solvable limit, the inhomogeneous complex square well, is also identified.