论文标题
在没有$ \ Mathcal {pt} $对称性的情况下，骨髓系统中的旋转时间对称性和存在特殊点
Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of $\mathcal{PT}$ symmetry
论文作者
论文摘要
我们研究在存在激光泵送的情况下开放的骨髓系统的对称性。描述这些系统的非热汉密尔顿人可以是平等时间（$ {\ cal {pt}} $）在特殊情况下对称。表现出这种对称性的系统的特征是实现的能量光谱，并且可以显示出特殊的点，其中发生对称性的过渡。我们证明存在更通用的对称性类型，即旋转时间（$ {\ cal {rt}} $）对称性。我们观察到$ {\ cal {rt}} $ - 对称的非汉密尔顿汉密尔顿人表现出实用值的能量谱，可以通过对称性破坏使人单数。为了计算所研究的纤维音不可用的汉密尔顿人的光谱，我们采用基于玻感代数的对角线化方法。最后，我们列出了一个多功能设置规则，允许立即识别或构造$ {\ cal {rt}} $ - 对称的汉密尔顿人。我们认为，我们在$ {\ cal {rt}} $上的结果 - 对称的骨系统及其光谱奇点可以导致受$ {\ cal {pt}} $ - 对称系统的启发的新应用。
We study symmetries of open bosonic systems in the presence of laser pumping. Non-Hermitian Hamiltonians describing these systems can be parity-time (${\cal{PT}}$) symmetric in special cases only. Systems exhibiting this symmetry are characterised by real-valued energy spectra and can display exceptional points, where a symmetry-breaking transition occurs. We demonstrate that there is a more general type of symmetry, i.e., rotation-time (${\cal{RT}}$) symmetry. We observe that ${\cal{RT}}$-symmetric non-Hermitian Hamiltonians exhibit real-valued energy spectra which can be made singular by symmetry breaking. To calculate the spectra of the studied bosonic non-diagonalisable Hamiltonians we apply diagonalisation methods based on bosonic algebra. Finally, we list a versatile set rules allowing to immediately identifying or constructing ${\cal{RT}}$-symmetric Hamiltonians. We believe that our results on the ${\cal{RT}}$-symmetric class of bosonic systems and their spectral singularities can lead to new applications inspired by those of the ${\cal{PT}}$-symmetric systems.
