Resilience of ${\mathscr{P}}{\mathscr{T}}$ symmetry against stochasticity in a gain-loss balanced oscillator
Resilience of ${\mathscr{P}}{\mathscr{T}}$ symmetry against stochasticity in a gain-loss balanced oscillator
复制标题
${mathscr{P}}{mathscr{T}}$对称性对增益损失平衡振荡器中随机性的弹性
DOI：
10.1088/1367-2630/18/10/105001
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发表时间：
2016
影响因子：
3.3
通讯作者：
Lukovic M
中科院分区：
文献类型：
--
作者：
Lukovic M
我们研究了以随机时变增益和损失状态的形式加入经典谐振子的二分类噪声的影响，其持续时间从两个不同的指数等待时间分布中采样。尽管存在随机性，但稳定性准则可以在渐近时间限制内对许多实现进行平均时形成，并用于确定参数空间中的边界线，该边界线将振幅增长的区域与衰减的区域分开。此外，对称性的概念仍然适用于这种随机振荡器，我们用它来区分欠阻尼对称相位和过阻尼不对称相位。在前一种情况下，稳定极限的标志是增益和损失状态的平均持续时间相同，而在后一种情况下，需要更长的损失状态持续时间来保持系统稳定。过阻尼相具有施加位置-速度比锁定的有序结构，并且被视为欠阻尼相的相变，相反，欠阻尼相显示出广泛和更无序，但仍然是对称结构。我们还讨论了短时间限制以及位置和速度力矩的动力学，目的是揭示这个看似相当简单的机械系统所提供的极其丰富的动力学。目前所建立的概念可以推广和应用于光在具有非对称主动和被动介质随机分布区域的超材料和光纤中的传播稳定。
We investigate the effects of dichotomous noise added to a classical harmonic oscillator in the form of stochastic time-dependent gain and loss states, whose durations are sampled from two distinct exponential waiting time distributions. Despite the stochasticity, stability criteria can be formulated when averaging over many realizations in the asymptotic time limit and serve to determine the boundary line in parameter space that separates regions of growing amplitudes from those of decaying ones. Furthermore, the concept ofsymmetry remains applicable for such a stochastic oscillator and we use it to distinguish between an underdamped symmetric phase and an overdamped asymmetric phase. In the former case, the limit of stability is marked by the same average duration for the gain and loss states, whilst in the the latter case, a higher duration of the loss state is necessary to keep the system stable. The overdamped phase has an ordered structure imposing a position-velocity ratio locking and is viewed as a phase transition from the underdamped phase, which instead displays a broad and more disordered, but nevertheless,symmetric structure. We also address the short time limit and the dynamics of the moments of the position and the velocity with the aim of revealing the extremely rich dynamics offered by this apparently quite simple mechanical system. The notions established so far may be extended and applied in the stabilization of light propagation in metamaterials and optical fibres with randomly distributed regions of asymmetric active and passive media.