具有保守噪声的Toda晶格的热导率
Thermal conductivity of the Toda lattice with conservative noise
摘要：
本文研究了一维Toda晶格在保能量和动量随机动力学扰动下的热导率。随机噪声的强度由参数$γ$控制。我们发现，热输运是异常的，并根据$κ(n) \sim n^α$，与$0 < α\leq 1/2$的链的长度$n$的热导率发散。特别地，未扰动的Toda链的弹道热传导被破坏。此外，发散指数$α$依赖于$γ$。
英文摘要：
We study the thermal conductivity of the one dimensional Toda lattice perturbed by a stochastic dynamics preserving energy and momentum. The strength of the stochastic noise is controlled by a parameter $γ$. We show that heat transport is anomalous, and that the thermal conductivity diverges with the length $n$ of the chain according to $κ(n) \sim n^α$, with $0 < α\leq 1/2$. In particular, the ballistic heat conduction of the unperturbed Toda chain is destroyed. Besides, the exponent $α$ of the divergence depends on $γ$.
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