Indiana University Purdue University Indianapolis (IUPUI), Indianapolis, 46202, USA.
Sci Rep. 2018 Jan 8;8(1):44. doi: 10.1038/s41598-017-18589-z.
Open, non-equilibrium systems with balanced gain and loss, known as parity-time ([Formula: see text])-symmetric systems, exhibit properties that are absent in closed, isolated systems. A key property is the [Formula: see text]-symmetry breaking transition, which occurs when the gain-loss strength, a measure of the openness of the system, exceeds the intrinsic energy-scale of the system. We analyze the fate of this transition in disordered lattices with non-Hermitian gain and loss potentials ±iγ at reflection-symmetric sites. Contrary to the popular belief, we show that the [Formula: see text]-symmetric phase is protected in the presence of a periodic disorder which leads to a positive [Formula: see text]-symmetry breaking threshold. We uncover a veiled symmetry of such disordered systems that is instrumental for the said protection, and show that this symmetry leads to new localization behavior across the [Formula: see text]-symmetry breaking transition. We elucidate the interplay between such localization and the [Formula: see text]-symmetry breaking phenomena in disordered [Formula: see text]-symmetric lattices, with Hermitian disorder or gain-loss disorder, and support our conclusions with a beampropagation- method analysis. Our theoretical predictions provide avenues for experimental realizations of -symmetric systems with engineered disorder.
开非平衡系统，具有平衡增益和损耗，被称为宇称时间（PT）对称系统，具有在封闭、孤立系统中不存在的性质。一个关键性质是 PT 对称破缺转变，当增益损耗强度，即系统开放性的度量，超过系统的固有能量尺度时，就会发生这种转变。我们在具有非厄米增益和损耗势 ±iγ 的反射对称点的无序晶格中分析了这种转变的命运。与普遍的看法相反，我们表明，在存在周期性无序的情况下，PT 对称相是受到保护的，这导致了正的 PT 对称破缺阈值。我们揭示了这种无序系统的一个隐蔽对称性，它对上述保护是至关重要的，并表明这种对称性导致了在 PT 对称破缺转变过程中出现新的局域化行为。我们阐明了在具有厄米或增益损耗无序的无序 PT 对称晶格中，这种局域化和 PT 对称破缺现象之间的相互作用，并通过光束传播方法分析支持了我们的结论。我们的理论预测为具有工程化无序的 -对称系统的实验实现提供了途径。
