论文标题
连接活动和被动$ \ Mathcal {pt} $ - 对称浮点调制模型
Connecting active and passive $\mathcal{PT}$-symmetric Floquet modulation models
论文作者
论文摘要
在过去的十年中，非热汉密尔顿人描述的具有增益，损失或两者兼而有之的开放系统一直是研究领域。特别是，具有平等时间（$ \ Mathcal {pt} $）的对称性的汉密尔顿人动态稳定的不间断对称性稳定性，完全真实的特征谱将其呈现为复杂的共轭对，作为非敏捷性的强度增加。通过将$ \ MATHCAL {PT} $ - 对称系统进行定期（FLOQUET）驾驶，可以极大地影响动态稳定性的制度，从而导致$ \ Mathcal {pt} $对称性破坏过渡的频率依赖性阈值。我们提出了一个与时间相关的$ \ mathcal {pt} $ - 对称的汉密尔顿式的简单模型，该模型平稳地连接了静态案例，$ \ MATHCAL {pt} $ - 对称的floquet case和中性 - $ \ natercal {pt} $ - 对称案例。我们通过分析和数值分析每种情况下的$ \ MATHCAL {pt} $相图，并显示$ \ Mathcal {pt} $ - 损坏的slivers（$ \ nathcal {pt} $ - 对称 - 对称）相位延伸到名义上的低（高）非热门区域。
Open systems with gain, loss, or both, described by non-Hermitian Hamiltonians, have been a research frontier for the past decade. In particular, such Hamiltonians which possess parity-time ($\mathcal{PT}$) symmetry feature dynamically stable regimes of unbroken symmetry with completely real eigenspectra that are rendered into complex conjugate pairs as the strength of the non-Hermiticity increases. By subjecting a $\mathcal{PT}$-symmetric system to a periodic (Floquet) driving, the regime of dynamical stability can be dramatically affected, leading to a frequency-dependent threshold for the $\mathcal{PT}$-symmetry breaking transition. We present a simple model of a time-dependent $\mathcal{PT}$-symmetric Hamiltonian which smoothly connects the static case, a $\mathcal{PT}$-symmetric Floquet case, and a neutral-$\mathcal{PT}$-symmetric case. We analytically and numerically analyze the $\mathcal{PT}$ phase diagrams in each case, and show that slivers of $\mathcal{PT}$-broken ($\mathcal{PT}$-symmetric) phase extend deep into the nominally low (high) non-Hermiticity region.
