论文标题
积分变换和$ \ Mathcal {pt} $ - 对称性汉密尔顿人
Integral Transforms and $\mathcal{PT}$-symmetric Hamiltonians
论文作者
论文摘要
由傅立叶变换两倍的事实激发了均等操作员的角色。我们在$ \ Mathcal {pt} $ - 对称的哈密顿式的情况下系统地研究积分转换。首先，我们获得了一个封闭的分析公式，用于一般$ \ Mathcal {pt} $ - 对称性汉密尔顿的指数傅立叶变换。使用Segal-Bargmann变换，我们研究了傅立叶变换对原始汉密尔顿原征的影响。作为立即应用，我们评论了非铁旋转链的全体形态表示，其中汉密尔顿操作员是根据分析相空间坐标及其在巴格曼空间中的部分衍生物来编写的，而不是在矢量希尔伯特空间中的矩阵。最后，我们讨论了整体变换在Swanson Hamiltonian的研究中的效果。
Motivated by the fact that twice the Fourier transform plays the role of parity operator. We systematically study integral transforms in the case of $\mathcal{PT}$-symmetric Hamiltonian. First, we obtain a closed analytical formula for the exponential Fourier transform of a general $\mathcal{PT}$-symmetric Hamiltonian. Using the Segal-Bargmann transform, we investigate the effect of the Fourier transform on the eigenfunctions of the original Hamiltonian. As an immediate application, we comment on the holomorphic representation of non-Hermitian spin chains, in which the Hamiltonian operator is written in terms of analytical phase-space coordinates and their partial derivatives in the Bargmann space rather than matrices in the vector Hilbert space. Finally, we discuss the effect of integral transforms in the study of the Swanson Hamiltonian.
