论文标题
在驱动正弦模型中的混沌孤子
Chaotic solitons in driven sine-Gordon model
论文作者
论文摘要
一维标量场理论中静态孤子的曲线满足了与多维力学中虚拟粒子的轨迹相同的方程式。我们认为，如果各自的机械运动混乱，孤子的结构和特性本质上是不同的。这发生在多场模型和具有空间依赖电势的模型中。我们使用外部Dirac梳子电势中使用单场正弦戈登模型来说明我们的发现。首先，我们表明不同“混乱”孤子的数量随长度而成倍增长，而增长率与机械系统的拓扑熵有关。其次，稳定孤子的场值形成分形。我们计算其盒子计数尺寸。第三，我们证明了分形中场值的分布与类似机械系统的度量熵有关。
Profiles of static solitons in one-dimensional scalar field theory satisfy the same equations as trajectories of a fictitious particle in multidimensional mechanics. We argue that the structure and properties of the solitons are essentially different if the respective mechanical motions are chaotic. This happens in multifield models and models with spatially dependent potential. We illustrate our findings using one-field sine-Gordon model in external Dirac comb potential. First, we show that the number of different "chaotic" solitons grows exponentially with their length, and the growth rate is related to the topological entropy of the mechanical system. Second, the field values of stable solitons form a fractal; we compute its box-counting dimension. Third, we demonstrate that the distribution of field values in the fractal is related to the metric entropy of the analogous mechanical system.
