论文标题
在缓慢变化条件下的动态变化：量子Kruskal-Neishtadt-Henrard定理
Dynamical change under slowly changing conditions: the quantum Kruskal-Neishtadt-Henrard theorem
论文作者
论文摘要
当恒定能量轮廓分成单独的轮廓时，绝热近似经典地分解，迫使系统选择遵循哪个女儿轮廓；这些选择通常代表质性不同的行为，因此缓慢变化的条件会引起动态突然而急剧的变化。 Kruskal-Henrard-Neishtadt定理将每种选择的概率与不同轮廓所包围的相空间区域发生变化的速率联系起来。这代表了封闭系统力学中的连接，并且没有动态混乱，在自发变化和相位空间度量的增加之间，这是热力学第二定律所要求的。相比之下，量子在机械上，动态隧道允许通过经典的能量轮廓分裂，可以使绝热性持续，以使参数变化非常缓慢。经典和绝热的限制无法通勤。在这里，我们表明，由于单位性，Kruskal-Neishtadt-Henrard定理的一种量子形式仍然存在。
Adiabatic approximations break down classically when a constant-energy contour splits into separate contours, forcing the system to choose which daughter contour to follow; the choices often represent qualitatively different behavior, so that slowly changing conditions induce a sudden and drastic change in dynamics. The Kruskal-Henrard-Neishtadt theorem relates the probability of each choice to the rates at which the phase space areas enclosed by the different contours are changing. This represents a connection within closed-system mechanics, and without dynamical chaos, between spontaneous change and increase in phase space measure, as required by the Second Law of Thermodynamics. Quantum mechanically, in contrast, dynamical tunneling allows adiabaticity to persist, for very slow parameter change, through a classical splitting of energy contours; the classical and adiabatic limits fail to commute. Here we show that a quantum form of the Kruskal-Neishtadt-Henrard theorem holds nonetheless, due to unitarity.
