Habib Salman, Bhattacharya Tanmoy, Greenbaum Benjamin, Jacobs Kurt, Shizume Kosuke, Sundaram Bala
MS B285, Theoretical Division, The University of California, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Ann N Y Acad Sci. 2005 Jun;1045:308-32. doi: 10.1196/annals.1350.026.
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.
在一些人看来，混沌与量子力学之间的关系有些不和谐，甚至可以说是充满争议的。然而，许多混淆可能源于使用形式分析进行的不恰当比较。相比之下，我们这里的出发点是，完整的动力学描述需要全面理解被测系统的演化，这对于解释实际实验结果是必要的。当然，无论是在经典力学还是量子力学中，都是如此。由于物理状态的演化现在取决于测量结果，即使在分布函数层面，此类系统的动力学本质上也是非线性的。由于这一特性，从物理角度更完整的处理揭示了动力学状态的存在，比如混沌，而这在（未被观测的）线性情况中并无直接对应。此外，这种处理方式有助于理解在轨迹层面以及分布函数层面，观测到的量子系统的动力学如何能产生有效的经典行为。最后，我们有一个惊人的预测，即来自被测量子系统的时间序列在远离经典区域时可能是混沌的，其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进行检验。
