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摘要翻译：
孤立多体量子系统的时间动力学一直是一个难以捉摸的课题。然而，最近，对这个问题的有意义的实验研究终于成为可能，也激发了理论兴趣。量子统计力学的基础也许最迫切需要在这一领域取得进展。之所以如此，是因为在一般孤立系统中，人们期望非平衡动力学本身会导致热化：一种松弛到宏观量的值是静止的状态，对于差别很大的初始条件是普遍的，并且通过统计力学的经时间检验的配方是可预测的。然而，在某种意义上，多体量子力学的什么特征使量子热化成为可能并不明显，就像动力学混沌使经典热化成为可能一样。例如，动力学混沌本身不可能发生在一个孤立的量子系统中，在这个系统中，时间演化是线性的，频谱是离散的。最近的一些研究强调了新的规则可以适用于这种情况，甚至表明统计力学可能会对这种系统中的松弛结果做出错误的预测。在这里，我们证明了一个孤立的泛型量子多体系统实际上确实松弛到一个由标准统计力学处方很好描述的状态。此外，我们还证明了时间演化本身在弛豫中只起辅助作用，而热化则发生在由J.M.首先提出的单个本征态的水平上。Deutsch和M.Srednicki。这种本征态热化方案的一个引人注目的结果是，单个多体本征态的知识足以计算热平均值--微正则能量窗中的任何本征态都可以，因为它们都给出了相同的结果。
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英文标题：
《Thermalization and its mechanism for generic isolated quantum systems》
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作者：
Marcos Rigol, Vanja Dunjko, Maxim Olshanii
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最新提交年份：
2009
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
Time dynamics of isolated many-body quantum systems has long been an elusive subject. Very recently, however, meaningful experimental studies of the problem have finally become possible, stimulating theoretical interest as well. Progress in this field is perhaps most urgently needed in the foundations of quantum statistical mechanics. This is so because in generic isolated systems, one expects nonequilibrium dynamics on its own to result in thermalization: a relaxation to states where the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable through the time-tested recipe of 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. For example, dynamical chaos itself cannot occur in an isolated quantum system, where time evolution is linear and the spectrum is discrete. Underscoring that new rules could apply in this case, some recent studies even suggested that statistical mechanics may give wrong predictions for the outcomes of relaxation in such systems. Here we demonstrate that an isolated generic quantum many-body system does in fact 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 happens instead at the level of individual eigenstates, as first proposed by J.M. Deutsch and M. Srednicki. A striking consequence of this eigenstate thermalization scenario is that the knowledge of a single many-body eigenstate suffices to compute thermal averages-any eigenstate in the microcanonical energy window will do, as they all give the same result.
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PDF链接：
https://arxiv.org/pdf/708.1324
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