论文标题
古典哈密顿时间晶体的出处
Provenance of classical Hamiltonian time crystals
论文作者
论文摘要
具有保守电荷的古典哈密顿系统和具有限制性的汉密尔顿系统经常描述伴奏前歧管上的动力学。在这里，我们表明，预选前歧管也是描述保存哈密顿时间晶体的自主能量的合适阶段。我们解释了时间晶体的发生如何与自发破裂的对称性的更广泛的概念有关。在时间晶体的情况下，对称性破裂发生在动态环境中。然后，我们详细分析了两个时间晶体汉密尔顿动力学的示例。第一个示例是一个分段线性封闭的字符串，其动力学由与膜稳定性有关的Lie-poisson括号和汉密尔顿式的动力学决定。我们解释了Lie-poisson支架的下降到时间结晶前隔透明支架，我们表明汉密尔顿动力学支持两个阶段。在一个阶段，我们有一个时间晶体，在另一阶段，没有时间晶体。第二个例子是Q-ball Lagrangian的离散的哈密顿变体，该变体的时间依赖于非亲寻孤子。我们解释了Q-ball是如何变成时间晶体的，我们构建了时间晶体Q-balls的示例。
Classical Hamiltonian systems with conserved charges and those with constraints often describe dynamics on a pre-symplectic manifold. Here we show that a pre-symplectic manifold is also the proper stage to describe autonomous energy conserving Hamiltonian time crystals. We explain how the occurrence of a time crystal relates to the wider concept of spontaneously broken symmetries; in the case of a time crystal, the symmetry breaking takes place in a dynamical context. We then analyze in detail two examples of time crystalline Hamiltonian dynamics. The first example is a piecewise linear closed string, with dynamics determined by a Lie-Poisson bracket and Hamiltonian that relates to membrane stability. We explain how the Lie-Poisson brackets descents to a time crystalline pre-symplectic bracket, and we show that the Hamiltonian dynamics supports two phases; in one phase we have a time crystal and in the other phase time crystals are absent. The second example is a discrete Hamiltonian variant of the Q-ball Lagrangian of time dependent non-topological solitons. We explain how a Q-ball becomes a time crystal, and we construct examples of time crystalline Q-balls.
