具有真实势的层状晶体中的超声速超离散扭结
Ultradiscrete kinks with supersonic speed in a layered crystal with realistic potentials
摘要：
本文建立了硅酸盐云母晶体中阳离子层中非线性局域激发-超声扭结的动力学模型。我们从纯粹的静电库仑相互作用出发，加入Ziegler-Biersack-Littmark短程排斥势和晶格中其他原子产生的周期势。这种方法允许构建可以在大范围的能量和速度内在晶格中传播的超声扭结。在高能量的晶格扭折中，粒子间距是物理上合理的值。周期晶格势的引入使得扭结以单一的速度和能量传播，这与激发条件无关。所发现的扭结是超离散的，可以用“魔波数”$q\simeq 2π/3a$来描述，这是以前在费米-帕斯塔-乌拉姆晶格中的非线性正弦波和超声扭结中发现的。超音速扭结的极端离散性，基本上是两个粒子同时运动，允许解释它们的双扭结结构。超声扭结的能量介于β衰变中$^{40}$ K反冲的可能来源和实验发现的边界处原子弹射所需的能量之间。
英文摘要：
We develop a dynamical model of the propagating nonlinear localized excitations, supersonic kinks, in the cation layer in a silicate mica crystal. We start from purely electrostatic Coulomb interaction and add the Ziegler-Biersack-Littmark short-range repulsive potential and the periodic potential produced by other atoms of the lattice. This approach allows the construction of supersonic kinks which can propagate in the lattice within a large range of energies and velocities. The interparticle distances in the lattice kinks with high energy are physically reasonable values. The introduction of the periodic lattice potential results in the important feature that the kinks propagate with a single velocity and a single energy which are independent on the excitation conditions. The found kinks are ultra-discrete and can be described with the "magic wave number" $q\simeq 2π/3a$, which was previously revealed in the nonlinear sinusoidal waves and supersonic kinks in the Fermi-Pasta-Ulam lattice. The extreme discreteness of the supersonic kinks, with basically two particles moving at the same time, allows the interpretation of their double-kink structure. The energy of the supersonic kinks is between the possible source of $^{40}$K recoil in beta decay and the energy necessary for the ejection of an atom at the border as has been found experimentally.
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