论文标题
一维量子系统中松弛命运的不可证明性
Undecidability of the fate of relaxation in one-dimensional quantum systems
论文作者
论文摘要
我们研究了孤立的量子多体系统中的松弛动力学。松弛后可观察的固定值是量子热化领域研究的话题，因为热化是一种弛豫现象，在这种现象中，这种固定值与平衡值一致。因此，计算量子多体系统中的固定值被认为是一个重要问题。但是，我们证明了量子多体系统中的固定值是无法理解的。更确切地说，我们表明，固定值是否在给定值附近是一个不可决定的问题。当我们将系统限制到具有最近邻邻互动的一维移位系统时，我们的不确定结果仍然得到满足，我们的初始状态是单个站点上一个状态状态的初始状态，并且我们可观察到可观察到的一体偏移。该结果清楚地表明，在给定的量子多体系统中没有一般定理或程序来决定存在或不存在热化。
We investigate the relaxation dynamics in an isolated quantum many-body system. The stationary value of an observable after relaxation is a topic of researches in the field of quantum thermalization, since thermalization is a relaxation phenomena where this stationary value coincides with the equilibrium value. Therefore, computing the stationary value in quantum many-body systems is regarded as an important problem. We, however, prove that the stationary value in quantum many-body systems is incomputable. More precisely, we show that whether the stationary value is in the vicinity of a given value or not is an undecidable problem. Our undecidable result is still satisfied when we restrict our system to a one-dimensional shift-invariant system with nearest-neighbor interaction, our initial state to a product state of a state on a single site, and our observable to a shift-sum of a one-body observable. This result clearly shows that there is no general theorem or procedure to decide the presence or absence of thermalization in a given quantum many-body system.
