Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases
Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases
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DOI：
10.1103/physrevx.5.041043
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发表时间：
2015-12-16
影响因子：
12.5
通讯作者：
Konik, R. M.
中科院分区：
文献类型：
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作者：
Brandino, G. P.;Caux, J. -S.;Konik, R. M.
量子多体系统中的实时动力学本质上是复杂的，因此难以预测。然而，有一组特殊的系统，这些动力学在理论上是容易处理的：可积模型。这样的模型拥有超越能量和动量的非平凡守恒量。这些量被认为控制低维原子气体以及量子自旋链中的动力学和热化。但是，当导致额外守恒量存在的特殊对称性被打破时，会发生什么呢？如果断裂很弱，是否有任何数量的记忆？在这里，在弱可积性破缺的存在下，我们证明了有可能构造剩余拟守恒量，从而为KAM定理及其伴随的Nekhoreshev估计提供了一个量子模拟。我们证明了这种结构明确的背景下，在一维玻色气体的量子猝灭，并认为这些quasiconserved量可以探测实验。
Real-time dynamics in a quantum many-body system are inherently complicated and hence difficult to predict. There are, however, a special set of systems where these dynamics are theoretically tractable: integrable models. Such models possess nontrivial conserved quantities beyond energy and momentum. These quantities are believed to control dynamics and thermalization in low-dimensional atomic gases as well as in quantum spin chains. But what happens when the special symmetries leading to the existence of the extra conserved quantities are broken? Is there any memory of the quantities if the breaking is weak? Here, in the presence of weak integrability breaking, we show that it is possible to construct residual quasiconserved quantities, thus providing a quantum analog to the KAM theorem and its attendant Nekhoreshev estimates. We demonstrate this construction explicitly in the context of quantum quenches in one-dimensional Bose gases and argue that these quasiconserved quantities can be probed experimentally.