量子捕食者-猎物动力学：高斯系综分析
Quantum prey-predator dynamics: a gaussian ensemble analysis
AI总结：
本文在 Weyl-Wigner 量子力学框架下，利用高斯系综解析评估 Lotka-Volterra 哈密顿量描述的捕食者-猎物动力学，发现量子和高斯统计参数会改变系统的稳定性准则与时间演化模式。
摘要：
在量子力学提供的多种视角下，用于建模竞争性生态系统和自组织结构的量子框架已被广泛研究。这包括在 Weyl-Wigner 量子力学框架下对相空间中捕食者-猎物竞争动力学的描述。在这种情况下，从由 Lotka-Volterra (LV) 哈密顿量描述的经典动力学出发，被统计高斯系综卷积的量子态可以得到解析评估。随后可以识别出捕食者-猎物动力学在平衡与稳定性模式上的量子修正。这些修正包括对 LV 动力学平衡点驱动因素的量子畸变，这些畸变通过从初始哈密顿背景中获得的 Wigner 流通量进行量化。此外，对于高度局域于平衡点周围的高斯系综，稳定性性质被证明会受到涌现的拓扑量子域的影响；在某些情况下，这可能导致灭绝与复苏场景，或导致在微观系统中被识别为量子可观测量的捕食者和猎物智能体的永久共存。结论表明，量子和高斯统计驱动参数会影响此类类微生物群落的稳定性准则和时间演化模式。
英文摘要：
Quantum frameworks for modeling competitive ecological systems and self-organizing structures have been investigated under multiple perspectives yielded by quantum mechanics. These comprise the description of the phase-space prey-predator competition dynamics in the framework of the Weyl-Wigner quantum mechanics. In this case, from the classical dynamics described by the Lotka-Volterra (LV) Hamiltonian, quantum states convoluted by statistical gaussian ensembles can be analytically evaluated. Quantum modifications on the patterns of equilibrium and stability of the prey-predator dynamics can then be identified. These include quantum distortions over the equilibrium point drivers of the LV dynamics which are quantified through the Wigner current fluxes obtained from an onset Hamiltonian background. In addition, for gaussian ensembles highly localized around the equilibrium point, stability properties are shown to be affected by emergent topological quantum domains which, in some cases, could lead either to extinction and revival scenarios or to the perpetual coexistence of both prey and predator agents identified as quantum observables in microscopic systems. Conclusively, quantum and gaussian statistical driving parameters are shown to affect the stability criteria and the time evolution pattern for such microbiological-like communities.
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