论文标题
量子热化的不确定性
Undecidability in quantum thermalization
论文作者
论文摘要
在孤立的量子多体系统中对热化的研究具有悠久的历史，可以追溯到发展统计力学的时代。自然界中大多数量子多体系统都被认为可以热化，而有些则从未达到热平衡。中心问题是澄清给定的系统是否热拟化，该系统以前已经解决但未解决。在这里，我们表明这个问题是不确定的。当系统仅限于具有最接近邻居相互作用的一维移位系统时，最终的不确定性甚至适用，并且初始状态是固定的乘积状态。我们构建了一个编码可逆通用图灵机的动力学的哈密顿族人家族，放松过程的命运会大大变化，具体取决于图灵机器是否停止。我们的结果表明，没有一般定理，算法或系统的程序来确定任何给定的哈密顿量中存在或不存在热化。
The investigation of thermalization in isolated quantum many-body systems has a long history, dating back to the time of developing statistical mechanics. Most quantum many-body systems in nature are considered to thermalize, while some never achieve thermal equilibrium. The central problem is to clarify whether a given system thermalizes, which has been addressed previously, but not resolved. Here, we show that this problem is undecidable. The resulting undecidability even applies when the system is restricted to one-dimensional shift-invariant systems with nearest-neighbour interaction, and the initial state is a fixed product state. We construct a family of Hamiltonians encoding dynamics of a reversible universal Turing machine, where the fate of a relaxation process changes considerably depending on whether the Turing machine halts. Our result indicates that there is no general theorem, algorithm, or systematic procedure determining the presence or absence of thermalization in any given Hamiltonian.
