时变SU(1,1)和SU(2)系统的超越PT对称的非厄米哈密顿量——伪不变理论中的精确解和几何相位

Q2 Physics and Astronomy Physics Open Pub Date : 2022-12-01 DOI:10.1016/j.physo.2022.100126

Nadjat Amaouche , Maroua Sekhri , Rahma Zerimeche , Mustapha Maamache , J.-Q. Liang

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摘要

本文研究了由SU(1,1)和SU(2)生成子组成的时变非厄米哈密顿量。前一个哈密顿量是PT对称的，而后一个不是。提出了一个时变非酉算子来构造非厄米不变量，并验证了该非厄米不变量是具有实数特征值的伪厄米不变量。对SU(1,1)和SU(2)系统用伪厄密不变算子的特征态统一求得了精确解。在此基础上，推导出了可分为动态相位和几何相位的Lewis-Riesenfeld相位。分析结果与文献中相应的厄米哈密顿量一致。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Non-Hermitian Hamiltonian beyond PT symmetry for time-dependent SU(1,1) and SU(2) systems — Exact solution and geometric phase in pseudo-invariant theory

In this paper we investigate time-dependent non-Hermitian Hamiltonians, which consist of $S U (1, 1)$ and $S U (2)$ generators. The former Hamiltonian is PT symmetric but the latter one is not. A time-dependent non-unitary operator is proposed to construct the non-Hermitian invariant, which is verified as pseudo-Hermitian with real eigenvalues. The exact solutions are obtained in terms of the eigenstates of the pseudo-Hermitian invariant operator for both the $S U (1, 1)$ and $S U (2)$ systems in a unified manner. Then, we derive the Lewis–Riesenfeld (LR) phase, which can be separated into the dynamic and the geometrical phases. The analytical results are well consistent with those of the corresponding Hermitian Hamiltonians reported in the literature.