标题： 具有Kolmogorov-Arnold-Moser相空间结构系统的热传导 显示英文标题

标题： Heat conduction in systems with Kolmogorov-Arnold-Moser phase space structure

摘要： 我们研究由两个正弦波壁形成的弹道通道中的热传导以及相应无限长通道中的粒子扩散；后者系统具有无限视野，即粒子可以在不与波浪形墙壁碰撞的情况下行进任意距离。 对于小的波幅，热量载体的动力学是规则的，并使用有效势得到了温度分布和热流的解析结果。 该研究还提出了一种适用于任何波幅的温度分布公式。 当动力学是规则的时候，存在弹道导电性和弹道扩散。 相关动力系统的庞加莱图（无限长通道）在波幅增加时表现出向混沌的一般性转变。当没有Kolmogorov-Arnold-Moser（KAM）曲线来阻止所有混沌区域的连接时，均方位移随时间t渐近地增长为tln(t)。 显示英文摘要

摘要： We study heat conduction in a billiard channel formed by two sinusoidal walls and the diffusion of particles in the corresponding channel of infinite length; the latter system has an infinite horizon, i.e., a particle can travel an arbitrary distance without colliding with the rippled walls. For small ripple amplitudes, the dynamics of the heat carriers is regular and analytical results for the temperature profile and heat flux are obtained using an effective potential. The study also proposes a formula for the temperature profile that is valid for any ripple amplitude. When the dynamics is regular, ballistic conductance and ballistic diffusion are present. The Poincar\'e plots of the associated dynamical system (the infinitely long channel) exhibit the generic transition to chaos as ripple amplitude is increased.When no Kolmogorov-Arnold-Moser (KAM) curves are present to forbid the connection of all chaotic regions, the mean square displacement grows asymptotically with time t as tln(t).