平均场等耦合光子网络中的临界点现象和有限尺寸标度
Critical-point phenomena and finite-size scaling in mean-field equal-coupling photonic networks
摘要：
利用耦合模的非线性运动方程的时间演化，研究了多模等耦合光子网络中的平均场光学相变。类比相互作用的经典自旋的统计力学模型，建立在复值模式和两个组件的自旋之间的对应关系，被用来定义两个组件和单组件的序参量。进行全面的有限尺寸标度分析以估计由每模式的光能驱动的二阶相变的临界点和指数。系统的平衡特性进行比较，只要适用的精确结果。考虑到各种参数设置，我们的结果证实了跃迁的平均场性质，并建立了非线性能量密度相图中的临界线。临界尺度导致推断上临界尺寸$d_c=4$。与热力学量的联系是通过具有适当的零温度极限的动力学温度来建立的。在低温阶段（每模式低能量），自旋对齐。在高温阶段（每个模式的大能量），自旋彼此独立旋转。
英文摘要：
The mean-field optical phase transition in multimode equal-coupling photonic networks is studied by temporal evolution of the nonlinear equations of motion of the coupled modes. Analogies to statistical mechanics models of interacting classical spins, built upon the correspondence between complex-valued modes and two-component spins, are employed to define two-component and single-component order parameters. A comprehensive finite-size scaling analysis is performed to estimate critical points and exponents of a second-order phase transition, driven by the optical energy per mode. Equilibrium properties of the system are compared to exact results whenever applicable. Considering various parameter settings, our results confirm the mean-field nature of the transition and establish the critical line in the nonlinearity--energy-density phase diagram. Critical scaling leads to infer the upper critical dimension $d_c=4$. Connection to thermodynamic quantities is established by means of a kinetic temperature with appropriate zero-temperature limit. In the low temperature phase (low energy per mode), spins align. In the high temperature phase (large energy per mode), spins rotate independent of one another.
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