Chaos and Quantum Mechanics
Chaos and Quantum Mechanics
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DOI：
10.1196/annals.1350.026
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发表时间：
2005-05
影响因子：
5.2
通讯作者：
S. Habib;Tanmoy Bhattacharya;B. Greenbaum;K. Jacobs;K. Shizume;B. Sundaram
中科院分区：
文献类型：
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作者：
S. Habib;Tanmoy Bhattacharya;B. Greenbaum;K. Jacobs;K. Shizume;B. Sundaram
摘要：混沌与量子力学之间的关系在一些人的心目中有些不安，甚至是暴风雨。然而，许多混淆可能源于使用形式分析的不适当的比较。相反，我们这里的出发点是，一个完整的动力学描述需要充分理解被测量系统的演化，这是解释实际实验结果所必需的。这当然是对的，无论是经典的还是量子力学的。由于物理状态的演变现在取决于测量结果，因此即使在分布函数的水平上，这种系统的动力学本质上也是非线性的。由于这一特征，物理上更完整的处理揭示了动态状态的存在——比如混沌——在线性（未观察到的）情况下没有直接对应。此外，这种处理允许理解有效的经典行为是如何从观察到的量子系统的动力学中产生的，无论是在轨迹水平上还是在分布函数上。最后，我们得到了一个惊人的预测，即来自被测量量子系统的时间序列可能是远离经典状态的混沌，李雅普诺夫指数与经典值不同。这些预测可以在下一代实验中得到验证。
Abstract: The relationship between chaos and quantum mechanics has been somewhat uneasy—even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our starting point here is that a complete dynamical description requires a full understanding of the evolution of measured systems, necessary to explain actual experimental results. This is of course true, both classically and quantum mechanically. Because the evolution of the physical state is now conditioned on measurement results, the dynamics of such systems is intrinsically nonlinear even at the level of distribution functions. Due to this feature, the physically more complete treatment reveals the existence of dynamical regimes—such as chaos—that have no direct counterpart in the linear (unobserved) case. Moreover, this treatment allows for understanding how an effective classical behavior can result from the dynamics of an observed quantum system, both at the level of trajectories as well as distribution functions. Finally, we have the striking prediction that time‐series from measured quantum systems can be chaotic far from the classical regime, with Lyapunov exponents differing from their classical values. These predictions can be tested in next‐generation experiments.