脂质体-梅斯科夫-格里克量子脑模型中相变特征的分析
Characterization of Phase Transitions in a Lipkin-Meshkov-Glick Quantum Brain Model
AI总结：
该研究分析了受生物启发的量子脑模型中突触反馈对相变结构的影响，揭示了反馈机制如何改变临界边界并重塑集体临界性。
摘要：
在本工作中，我们分析了受脂质体-梅斯科夫-格里克框架启发的量子脑模型中相变的出现。其中，生物动机的突触反馈以非线性和状态依赖的方式调节集体相互作用。我们证明，纳入这种反向机制显著改变了相结构，相对于无反馈情况，使顺磁相扩大而铁磁相缩小。这种效应在存在纵向场时明显增强，因为反馈直接耦合到纵向磁化，导致临界边界有明显位移。我们从相空间的角度通过基态希斯米分布和韦尔熵来表征这些转变，这为局部化变化的定性诊断以及反馈引起的相图变形的定量评估提供了稳健的方法。此外，我们基于集体自旋取向的均场方程进行了显式的动态分析，这些方程与突触动力学自洽耦合，能够高保真地再现所考虑协议中集体可观测量的量子时间演化。总体而言，这些发现证实了该量子脑模型作为受控理论框架的适用性，用于阐明突触可塑性机制如何参数调制和重塑集体临界性。
英文摘要：
In this work we analyze the emergence of phase transitions in a quantum brain model inspired by the Lipkin-Meshkov-Glick framework, where biologically motivated synaptic feedback modulates the collective interaction in a nonlinear and state-dependent manner. We demonstrate that incorporating this retroactive mechanism substantially reshapes the phase structure, yielding an expansion of the paramagnetic phase at the expense of the ferromagnetic phases relative to the feedback-free scenario. This effect is markedly enhanced in the presence of a longitudinal field, as the feedback couples directly to the longitudinal magnetization, leading to an appreciable displacement of the critical boundaries. We characterize the ensuing transitions from a phase-space perspective by means of the ground-state Husimi distribution and the Wehrl entropy, which provide a robust diagnosis of qualitative changes in localization and enable a quantitative assessment of feedback-induced deformations of the phase diagram. Additionally, we perform an explicit dynamical analysis based on mean-field equations for the collective-spin orientation self-consistently coupled to the synaptic dynamics, which reproduces with high fidelity the quantum time evolution of collective observables for the protocols considered. Overall, these findings substantiate the suitability of this quantum brain model as a controlled theoretical framework for elucidating how synaptic plasticity mechanisms can parametrically tune and reshape collective criticality.
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