Mertens Franz G, Arévalo Edward, Bishop A R
Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Sep;72(3 Pt 2):036617. doi: 10.1103/PhysRevE.72.036617. Epub 2005 Sep 29.
We perform Langevin dynamics simulations for pulse solitons on atomic chains with anharmonic nearest-neighbor interactions. After switching off noise and damping after a sufficiently long time, the solitons are only influenced by the thermal phonon bath which had been created by the noise. The soliton diffusion constant D is considerably smaller than before the switch-off, and it is proportional to the square of the temperature T , in contrast to the diffusion due to the noise which is proportional to T . We derive a diffusion equation for a soliton which is scattered elastically in an ensemble of phonons and derive general expressions for D and for the drift velocity v(d) . These expressions can be evaluated for the case of the Toda lattice for which the soliton shift due to the phonon scattering is known explicitly. D is indeed proportional to T2 and agrees well with the simulation results, while v(d) is much smaller than the soliton velocity and cannot be measured in the simulations due to the large fluctuations of the soliton position. We express D in terms of soliton characteristics which are known also for solitons on other anharmonic chains in the continuum limit: namely, velocity, amplitude, and width. The results agree well with the simulations if the soliton shape is the same as in the Toda case. If the shape is different, only an estimate of the order of magnitude can be given.
我们对具有非谐近邻相互作用的原子链上的脉冲孤子进行朗之万动力学模拟。在足够长的时间后关闭噪声和阻尼，孤子仅受噪声产生的热声子浴影响。孤子扩散常数D比关闭之前小得多，并且它与温度T的平方成正比，这与与T成正比的噪声引起的扩散形成对比。我们推导了一个孤子在声子系综中弹性散射的扩散方程，并推导了D和漂移速度v(d)的一般表达式。对于托达晶格的情况，可以明确评估这些表达式，其中由于声子散射引起的孤子位移是已知的。D确实与T2成正比，并且与模拟结果吻合得很好，而v(d)比孤子速度小得多，并且由于孤子位置的大波动而无法在模拟中测量。我们根据孤子特性来表示D，在连续极限下，其他非谐链上的孤子也具有这些特性：即速度、幅度和宽度。如果孤子形状与托达晶格情况相同，结果与模拟吻合得很好。如果形状不同，则只能给出量级估计。
