论文标题
非相互作用系统中的轨迹相变：全动力学和随机能量模型
Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model
论文作者
论文摘要
我们研究了$ n $非相互作用的Ising旋转系统的随机动力学中时间添加随机可观察力的波动。我们主要考虑全部动力学的情况，在任何两个具有均匀速率的旋转配置之间进行过渡。我们表明，正态分布的配置的正态分布的随机函数的累积生成函数，即随机能量模型的能量函数（REM）的能量函数，在任何时间的轨迹的较大$ n $限制中具有相变。我们通过确定缩放累积生成函数的确切极限来证明这一点。这是通过将动态问题连接到对全部量子REM的光谱分析来完成的。我们还讨论了在数值模拟中观察到的有限$ n $校正。
We study the fluctuations of time-additive random observables in the stochastic dynamics of a system of $N$ non-interacting Ising spins. We mainly consider the case of all-to-all dynamics where transitions are possible between any two spin configurations with uniform rates. We show that the cumulant generating function of the time-integral of a normally distributed quenched random function of configurations, i.e., the energy function of the random energy model (REM), has a phase transition in the large $N$ limit for trajectories of any time extent. We prove this by determining the exact limit of the scaled cumulant generating function. This is accomplished by connecting the dynamical problem to a spectral analysis of the all-to-all quantum REM. We also discuss finite $N$ corrections as observed in numerical simulations.
