AI 中文总结
该研究针对宇称-时间二聚体，揭示杜芬非线性与噪声会导致线性宇称-时间未破缺相为瞬态，通过引入双光子损耗的非线性阻尼恢复全局随机稳定性，明确非厄米实验的稳定性源于恢复耗散而非宇称-时间对称。
AI 中文摘要
宇称-时间（$\boldsymbol{\textit{PT}}$）对称系统通过在耦合谐振器中平衡增益与损耗，展现出长寿命激发态，引发了广泛的理论研究兴趣与多样的实验实现。然而，实际物理实现中不可避免地会引入非线性与噪声，这要求对其全局长时间动力学进行严格的重新评估。本研究表明，哈密顿杜芬（Duffing）非线性将$\boldsymbol{\textit{PT}}$未破缺相限制在相空间中一个有限的非吸引区域内，因此不可避免的涨落会驱动首次通过逃逸进入失控轨迹，使得线性$\boldsymbol{\textit{PT}}$未破缺相成为纯粹的瞬态现象。随后，我们通过在增益振子上引入双光子损耗恢复了全局随机稳定性，这种非线性阻尼明确打破了精确$\boldsymbol{\textit{PT}}$对称，同时提供了真实的相空间吸引作用，生成了双稳态区域，其中模拟原始线性态的低振幅轨道与高振幅极限环共存。由此，我们确立了非厄米实验中稳定性的修正起源：观测到的长时间随机稳定性由固有恢复耗散而非光谱$\boldsymbol{\textit{PT}}$对称本身所决定。
英文摘要
Parity-time ($\mathcal{PT}$) symmetric systems exhibit long-lived excitations by balancing gain and loss in coupled resonators, driving extensive theoretical interest and diverse experimental realizations. Realistic physical implementations, however, inevitably introduce nonlinearities and noise. This mandates a rigorous reevaluation of their global long-time dynamics. In this work, we show that Hamiltonian Duffing nonlinearity restricts the $\mathcal{PT}$-unbroken phase to a finite, nonattracting region of phase space. Consequently, unavoidable fluctuations drive first-passage escape into runaway trajectories. This renders the linearly $\mathcal{PT}$-unbroken phase a purely transient phenomenon. We then recover global stochastic stability by introducing two-photon loss on the gain oscillator. This nonlinear damping explicitly breaks exact $\mathcal{PT}$ symmetry while supplying genuine phase-space attraction, generating a bistable regime where a low-amplitude orbit mimicking the original linear state coexists with a high-amplitude limit cycle. Thus, we establish a revised origin for stability in non-Hermitian experiments: the observed long-time stochastic stability is governed by inherent restoring dissipation rather than the spectral $\mathcal{PT}$ symmetry itself.
Comments6 pages (main), 3 figures (main) + Supplemental Material (6 pages, 2 figures)
