Herein, we propose a family of non-Hermitian Hamiltonians with real spectra other than the space-time reflection (PT) symmetric class, and discuss its application in the predator-prey ecological processes described by a generalized Lotka-Volterra equation. In the phase space, such a nonlinear equation could support both chaotic and localized dynamics separated by a dynamical critical point, which can be understood as a consequence of the interplay between the periodicity and non-Hermiticity of its effective Hamiltonian in the linearized equation of motion. Further, the dynamics at the critical point (e.g. the algebraic divergence,) can be understood as an exceptional point in the context of non-Hermitian physics. Applications to genuine quantum systems have also been discussed.

中文翻译：

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新的准厄米特哈密顿量家族及其在捕食者-猎物耦合圈中的应用

在这里，我们提出了一个具有除时空反射（PT）对称类之外的真实光谱的非厄米哈密顿量族，并讨论了其在广义 Lotka-Volterra 方程描述的捕食者 - 猎物生态过程中的应用。在相空间中，这样的非线性方程可以支持由动力学临界点分隔的混沌和局部动力学，这可以理解为线性化运动方程中其有效哈密顿量的周期性和非赫密性相互作用的结果. 此外，临界点处的动力学（例如代数散度）可以理解为非厄米物理学背景下的一个例外点。还讨论了真正的量子系统的应用。