（3+1）维Skyrme模型的可积性和化学势
Integrability and chemical potential in the (3+1)-dimensional Skyrme model
摘要：
利用从（3+1）维Skyrme模型到Sine-Gordon模型的一个显着映射，我们构造了3+1维平坦时空中有限盒内Skyrmions以及Skyrmions-反Skyrmions束缚态的第一个解析例子.导出了这些Skyrmions-反Skyrmions束缚态个数的解析上界。我们计算了临界的同位旋化学势，超过这个势这些Skyrmions就不存在了。有了这些工具，我们还构建拓扑保护的时间晶体：时间周期的配置，其时间依赖性是由他们的非平凡的缠绕数保护。这些是Shapere和Wilczek思想的惊人实现。确定了这些时间晶体的临界同位旋化学势。
英文摘要：
Using a remarkable mapping from the original (3+1)dimensional Skyrme model to the Sine-Gordon model, we construct the first analytic examples of Skyrmions as well as of Skyrmions--anti-Skyrmions bound states within a finite box in 3+1 dimensional flat space-time. An analytic upper bound on the number of these Skyrmions--anti-Skyrmions bound states is derived. We compute the critical isospin chemical potential beyond which these Skyrmions cease to exist. With these tools, we also construct topologically protected time-crystals: time-periodic configurations whose time-dependence is protected by their non-trivial winding number. These are striking realizations of the ideas of Shapere and Wilczek. The critical isospin chemical potential for these time-crystals is determined.
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