相互作用原子链中的静态扭结
Static kinks in chains of interacting atoms
摘要：
本文从理论上分析了在周期晶格中通过排斥幂律势相互作用的粒子链中的拓扑孤子方程。从离散模型出发，对幂律指数$n \ge 1$进行梯度展开，得到连续极限下的扭结方程。幂律相互作用修改了正弦-戈登方程，导致系数乘以二阶导数（扭结宽度）的重新缩放，并增加了一个积分项。我们认为，积分项不影响扭结的局部性质，但它支配的行为在渐近。在中心的扭结行为是由一个正弦戈登方程和它的宽度往往与幂律指数增加。当相互作用是库仑排斥时，特别是，扭结宽度依赖于链的大小。我们定义了一个适当的热力学极限，并将我们的结果与现有的研究进行无限链。我们的形式主义允许一个系统地考虑到有限尺寸的影响，也缓慢变化的外部电位，例如在离子阱的曲率。
英文摘要：
We theoretically analyse the equation of topological solitons in a chain of particles interacting via a repulsive power-law potential and confined by a periodic lattice. Starting from the discrete model, we perform a gradient expansion and obtain the kink equation in the continuum limit for a power law exponent $n \ge 1$. The power-law interaction modifies the sine-Gordon equation, giving rise to a rescaling of the coefficient multiplying the second derivative (the kink width) and to an additional integral term. We argue that the integral term does not affect the local properties of the kink, but it governs the behaviour at the asymptotics. The kink behaviour at the center is dominated by a sine-Gordon equation and its width tends to increase with the power law exponent. When the interaction is the Coulomb repulsion, in particular, the kink width depends logarithmically on the chain size. We define an appropriate thermodynamic limit and compare our results with existing studies performed for infinite chains. Our formalism allows one to systematically take into account the finite-size effects and also slowly varying external potentials, such as for instance the curvature in an ion trap.
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