论文标题
一维不均匀的长距离交互的动力学理论，$ n $ n $系统，订单$ 1/n^{2} $没有集体效果
Kinetic theory of one-dimensional inhomogeneous long-range interacting $N$-body systems at order $1/N^{2}$ without collective effects
论文作者
论文摘要
由于其有限的粒子$ n $，远程相互作用的系统不可逆转地放松。在订单$ 1/n $的情况下，此过程由不均匀的Balescu--lenard方程描述。然而，该方程完全消失在具有单调频率且仅维持1：1共振的一维不均匀系统中。在可以忽略集体效果的限制中，我们为此系统得出了一个封闭的$ 1/n^{2} $碰撞运算符。我们详细介绍了它的属性，特别是它如何满足Boltzmann熵的$ H $ Theorem。我们还将其预测与直接$ n $ body模拟进行了比较。最后，我们展示了一类通用的远程交互潜力，这是$ 1/n^{2} $碰撞运算符完全消失的。
Long-range interacting systems irreversibly relax as a result of their finite number of particles, $N$. At order $1/N$, this process is described by the inhomogeneous Balescu--Lenard equation. Yet, this equation exactly vanishes in one-dimensional inhomogeneous systems with a monotonic frequency profile and sustaining only 1:1 resonances. In the limit where collective effects can be neglected, we derive a closed and explicit $1/N^{2}$ collision operator for such systems. We detail its properties highlighting in particular how it satisfies an $H$-theorem for Boltzmann entropy. We also compare its predictions with direct $N$-body simulations. Finally, we exhibit a generic class of long-range interaction potentials for which this $1/N^{2}$ collision operator exactly vanishes.
