一维盒子中理想经典粒子的弛豫
Relaxation of ideal classical particles in a one-dimensional box
摘要：
我们研究的确定性动力学的非相互作用的经典气体粒子局限于一个一维的盒子作为教学玩具模型的放松玻尔兹曼分布向平衡。硬的容器壁单独在很大程度上引起气体颗粒的均匀分布。对于速度分布的松弛，我们通过独立的散射体来模拟动态壁。马尔可夫性质保证了气体粒子在大时间内的稳定但不一定是热速度分布。我们确定的条件下，物理壁的静止速度分布是麦克斯韦分布。在我们的数值模拟中，我们用独立的谐振子来表示壁粒子。相应的动力学映射的振荡器与一个固定的相位（费米-乌拉姆加速器）是混乱的介观盒尺寸。
英文摘要：
We study the deterministic dynamics of non-interacting classical gas particles confined to a one-dimensional box as a pedagogical toy model for the relaxation of the Boltzmann distribution towards equilibrium. Hard container walls alone induce a uniform distribution of the gas particles at large times. For the relaxation of the velocity distribution we model the dynamical walls by independent scatterers. The Markov property guarantees a stationary but not necessarily thermal velocity distribution for the gas particles at large times. We identify the conditions for physical walls where the stationary velocity distribution is the Maxwell distribution. For our numerical simulation we represent the wall particles by independent harmonic oscillators. The corresponding dynamical map for oscillators with a fixed phase (Fermi--Ulam accelerator) is chaotic for mesoscopic box dimensions.
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