AI 中文总结
研究费米 - 帕斯塔 - 乌拉姆系统冷却过程，通过数值模拟发现弱随机阈值影响冷却，低于阈值时系统失衡，零温时有残余能量E₀，其对系统大小和冷却速率呈幂律依赖，近似为E₀ ∼ (ξN)²/³。
AI 中文摘要
在本工作中，我们对费米 - 帕斯塔 - 乌拉姆（FPU）系统的冷却过程进行了数值研究。此过程发生在FPU系统与温度T以特定冷却速率ξ降低的气体接触时。发现弱随机阈值的存在对冷却过程有显著影响，低于该阈值时，特定FPU能量大于其温度，即FPU系统失去平衡。在T→0极限下差异保持有限，使得FPU系统在零温度时保持残余能量E₀。数值模拟表明该能量对系统大小和冷却速率均呈现幂律依赖关系，近似为E₀ ∼ (ξN)²/³。
英文摘要
In this work, we numerically studied the cooling process of a Fermi--Pasta--Ulam system, which occurs when the FPU system is placed in contact with a gas whose temperature $T$ is reduced with a certain cooling rate $ξ$. It was found that the existence of a weak stochastic threshold has a significant impact on the cooling process, because below such a stochastic threshold the specific FPU energy is larger than its temperature, i.e., the FPU system falls out of equilibrium. The difference remains finite in the limit $T \to 0$, so that the FPU system maintains a residual amount of energy $E_0$ at vanishing temperature. Our numerical simulations reveal that this energy exhibits a power--law dependence on both the system size and the cooling rate, scaling approximately as $E_{0} \sim (ξN)^{2/3}$.
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