Thermalization and its mechanism for generic isolated quantum systems
Thermalization and its mechanism for generic isolated quantum systems
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DOI：
10.1038/nature06838
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发表时间：
2008-04-17
期刊：
影响因子：
64.8
通讯作者：
Olshanii, Maxim
中科院分区：
文献类型：
--
作者：
Rigol, Marcos;Dunjko, Vanja;Olshanii, Maxim
对孤立多体量子系统的时间演化的理解一直是难以捉摸的。最近，对这个问题有意义的实验研究（1,2）已经成为可能，激发了理论兴趣（3-7）。在一般的孤立系统中，非平衡动力学预计（8,9）会导致热化：一种松弛状态，在这种状态下，宏观量的值是平稳的，相对于广泛不同的初始条件是普遍的，并且可以使用统计力学进行预测。然而，多体量子力学的什么特征使量子热化成为可能，就像动力混沌使经典热化成为可能一样，这一点并不明显（10）。例如，动态混沌本身不能发生在一个孤立的量子系统中，其中时间演化是线性的，频谱是离散的（11）。最近的一些研究（4,5）甚至表明，统计力学可能对这类系统中的弛豫结果给出不正确的预测。在这里，我们证明了一般孤立量子多体系统确实松弛到一个由标准统计力学处方很好地描述的状态。此外，我们表明，时间演化本身在弛豫中仅起辅助作用，而热化反而发生在单个特征态的水平上，如Deutsch（12）和Srednicki（13）首先提出的那样。这个本征态-热化情景的一个显著结果，在我们的系统中得到了证实，那就是对单个多体本征态的了解足以计算热平均——微规范能量窗口中的任何本征态都可以，因为它们都给出相同的结果。
An understanding of the temporal evolution of isolated many-body quantum systems has long been elusive. Recently, meaningful experimental studies(1,2) of the problem have become possible, stimulating theoretical interest(3-7). In generic isolated systems, non- equilibrium dynamics is expected(8,9) to result in thermalization: a relaxation to states in which the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable using statistical mechanics. However, it is not obvious what feature of many- body quantum mechanics makes quantum thermalization possible in a sense analogous to that in which dynamical chaos makes classical thermalization possible(10). For example, dynamical chaos itself cannot occur in an isolated quantum system, in which the time evolution is linear and the spectrum is discrete(11). Some recent studies(4,5) even suggest that statistical mechanics may give incorrect predictions for the outcomes of relaxation in such systems. Here we demonstrate that a generic isolated quantum many- body system does relax to a state well described by the standard statistical- mechanical prescription. Moreover, we show that time evolution itself plays a merely auxiliary role in relaxation, and that thermalization instead happens at the level of individual eigenstates, as first proposed by Deutsch(12) and Srednicki(13). A striking consequence of this eigenstate- thermalization scenario, confirmed for our system, is that knowledge of a single many- body eigenstate is sufficient to compute thermal averages - any eigenstate in the microcanonical energy window will do, because they all give the same result.