标题： 精确可解的二维$\mathcal{PT}$对称模型 显示英文标题

标题： Exactly solvable $\mathcal{PT}$-symmetric models in two dimensions

摘要： 非厄米特的，$\mathcal{PT}$对称哈密顿量，在光学系统中被实验实现，能够准确模拟具有平衡、空间分离增益和损耗的开放玻色系统特性。 我们提出了一类精确可解的二维，$\mathcal{PT}$势，用于限制在圆形几何中的非相对论粒子。 我们表明，$\mathcal{PT}$对称性阈值可以通过引入第二个增益-损耗势或其厄米特对应物来调节。 我们的结果明确展示了二维情况下的$\mathcal{PT}$破裂具有丰富的相图，包含多个重新出现的$\mathcal{PT}$对称相。 显示英文摘要

摘要： Non-hermitian, $\mathcal{PT}$-symmetric Hamiltonians, experimentally realized in optical systems, accurately model the properties of open, bosonic systems with balanced, spatially separated gain and loss. We present a family of exactly solvable, two-dimensional, $\mathcal{PT}$ potentials for a non-relativistic particle confined in a circular geometry. We show that the $\mathcal{PT}$ symmetry threshold can be tuned by introducing a second gain-loss potential or its hermitian counterpart. Our results explicitly demonstrate that $\mathcal{PT}$ breaking in two dimensions has a rich phase diagram, with multiple re-entrant $\mathcal{PT}$ symmetric phases.