估计局部哈密顿动力学和连续量子随机游动的混合性质是PSPACE困难的
Estimating mixing properties of local Hamiltonian dynamics and continuous quantum random walks is PSPACE-hard
摘要：
（经典）遍历理论的一个主要课题是定性地研究动力系统的相空间如何被其动力学轨道穿透。我们根据4-定域哈密顿量和连续量子随机游动考虑相互作用量子比特系统的动力学。对于这些系统，可以使用时间平均的冯诺伊曼熵来表征相应轨道的混合性质，即，状态空间的哪一部分，以及它被轨道填充的均匀程度。我们表明，估计这个熵的问题是PSPACE-硬。
英文摘要：
A major topic of (classical) ergodic theory is to examine qualitatively how the phase space of dynamical systems is penetrated by the orbits of their dynamics. We consider interacting qubit systems with dynamics according to 4-local Hamiltonians and continuous quantum random walks. For these systems one could use the von Neumann entropy of the time-average to characterize the mixing properties of the corresponding orbits, i.e., what portion of the state space and how uniformly it is filled out by the orbits. We show that the problem of estimating this entropy is PSPACE-hard.
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