论文标题
古典哈密顿时间晶体 - 一般理论和简单的例子
Classical Hamiltonian Time Crystals -- General Theory And Simple Examples
论文作者
论文摘要
我们专注于具有连续对称性的哈密顿系统，以及在预叠式歧管上发生的动力学。我们解释了对称性如何被时间晶体自发打破，我们将其定义为可用的机械自由能的最小值，这同时是汉密尔顿方程的时间依赖性解决方案。这种时间统治自发对称性破裂的数学描述基于哈密顿流动空间中的摩尔斯摩尔斯理论概念。例如，我们分析了一个旨在建模多边形，分段线性封闭字符串的一般性时刻汉密尔顿人家族。 The vertices correspond to the locations of pointlike interaction centers;字符串类似于原子链，通过共价键将其连接在一起，以字符串的链接建模。我们认为，字符串的时间晶体特征可能会受到其拓扑的影响。为此，我们表明，一个打结的字符串通常比没有自我输入的字符串更时刻。我们还揭示了相空间拓扑与时间晶体动力学的发生之间的关系。为此，我们表明，在三个点粒子的情况下，时间晶体的存在可能与位于相空间中的狄拉克单子有关。我们的结果表明，可以通过封闭的，打结的分子环来实现哈密顿时间晶体的物理实例。
We focus on a Hamiltonian system with a continuous symmetry, and dynamics that takes place on a presymplectic manifold. We explain how the symmetry can become spontaneously broken by a time crystal, that we define as the minimum of the available mechanical free energy that is simultaneously a time dependent solution of Hamilton's equation. The mathematical description of such a timecrystalline spontaneous symmetry breaking builds on concepts of equivariant Morse theory in the space of Hamiltonian flows. As an example we analyze a general family of timecrystalline Hamiltonians that is designed to model polygonal, piecewise linear closed strings. The vertices correspond to the locations of pointlike interaction centers; the string is akin a chain of atoms, that are joined together by covalent bonds, modeled by the links of the string. We argue that the timecrystalline character of the string can be affected by its topology. For this we show that a knotty string is usually more timecrystalline than a string with no self-entanglement. We also reveal a relation between phase space topology and the occurrence of timecrystalline dynamics. For this we show that in the case of three point particles, the presence of a time crystal can relate to a Dirac monopole that resides in the phase space. Our results propose that physical examples of Hamiltonian time crystals can be realized in terms of closed, knotted molecular rings.
