无限大经典非简谐晶体的动力学
Dynamics of infinite classical anharmonic crystals
摘要：
我们考虑一个无界晶格，在这个晶格的每一点上的非谐振子，它与它的第一个邻居通过一对潜在的$V$相互作用，并受到潜在的回复力$U$。我们假设$U$和$V$是次数为$2σ_1$和$2σ_2$的偶次非负多项式。我们研究了这个系统的时间演化，控制当地的能量在时间上的增长，我们给出了一个非平凡的扰动的传播速度的限制。这是对$σ_1 \geq 2σ_2-1$的一些已知结果的$σ_1 < 2σ_2-1$情形的扩展。
英文摘要：
We consider an unbounded lattice and at each point of this lattice an anharmonic oscillator, that interacts with its first neighborhoods via a pair potential $V$ and is subjected to a restoring force of potential $U$. We assume that $U$ and $V$ are even nonnegative polynomials of degree $2σ_1$ and $2σ_2$. We study the time evolution of this system, with a control of the growth in time of the local energy, and we give a nontrivial bound on the velocity of propagation of a perturbation. This is an extension to the case $σ_1 < 2σ_2-1$ of some already known results obtained for $σ_1 \geq 2σ_2-1$.
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