Open systems with balanced gain and loss, described by parity-time PT-symmetric Hamiltonians have been deeply explored over the past decade. Most explorations are limited to finite discrete models (in real or reciprocal spaces) or continuum problems in one dimension. As a result, these models do not leverage the complexity and variability of two-dimensional continuum problems on a compact support. Here, we investigate eigenvalues of the Schrodinger equation on a disk with zero boundary condition, in the presence of constant, PT-symmetric, gain-loss potential that is confined to two mirror-symmetric disks. We find a rich variety of exceptional points, re-entrant PT-symmetric phases, and a non-monotonic dependence of the PT-symmetry breaking threshold on the system parameters. By comparing results of two model variations, we show that this simple model of a multi-core fiber supports propagating modes in the presence of gain and loss.

翻译：具有平衡增益与损耗的开放系统由宇称-时间（PT）对称哈密顿量描述，过去十年间已得到深入探索。然而，多数研究局限于有限离散模型（实空间或倒易空间）或一维连续介质问题。因此，这些模型未能充分利用二维连续介质问题在紧致支撑域中的复杂性与多样性。本文研究圆盘上零边界条件下薛定谔方程的特征值问题，其中存在局限于两个镜像对称圆盘内的恒定PT对称增益-损耗势。我们发现了一系列丰富的奇异点、可重入PT对称相位，以及PT对称破缺阈值对系统参数的非单调依赖性。通过比较两种模型变体的结果，我们证明这种简单的多芯光纤模型在存在增益与损耗的情况下能够支持传播模式。