Edge states of a diffusion equation in one dimension: Rapid heat conduction to the heat bath
Edge states of a diffusion equation in one dimension: Rapid heat conduction to the heat bath
复制标题
一维扩散方程的边缘状态：向热浴的快速热传导
DOI：
10.1103/physreve.105.024137
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Shusei Makino Takahiro Fukui Tsuneya Yoshida and Yasuhiro Hatsugai
中科院分区：
文献类型：
--
作者：
Hiromasa Wakao;Tsuneya Yoshida;Yasuhiro Hatsugai;Shusei Makino Takahiro Fukui Tsuneya Yoshida and Yasuhiro Hatsugai
对于扩散常数(热扩散率)随空间周期交替变化的系统，我们提出了一维扩散方程(热方程)。我们通过对角化哈密顿量，即具有交替扩散常数的拉普拉斯量，并利用其本征态展开温度分布，来求解给定初始分布的场(温度)分布的时间演化。我们表明，基本上存在有或没有边态的相。边缘状态影响着热浴周围的热传导。特别是，在短时间内将观察到热浴的快速换热，估计这对于该系统和由两种常见的金属如钛、锆和铝、金等组成的系统而言。我们还讨论了有效晶格模型，它简化了直到高能的边态计算。结果表明，这些高能边态也有助于在很短的时间内进行非常快速的热传导。
We propose a one-dimensional diffusion equation (heat equation) for systems in which the diffusion constant (thermal diffusivity) varies alternately with a spatial period. We solve the time evolution of the field (temperature) profile from a given initial distribution, by diagonalizing the Hamiltonian, i.e., the Laplacian with alternating diffusion constants, and expanding the temperature profile by its eigenstates. We show that there are basically phases with or without edge states. The edge states affect the heat conduction around heat baths. In particular, rapid heat transfer to heat baths would be observed in a short-time regime, which is estimated to befor thesystem andfor thesystem composed of two kinds of familiar metals such as titanium, zirconium, and aluminium, gold, etc. We also discuss the effective lattice model which simplifies the calculation of edge states up to high energy. It is suggested that these high-energy edge states also contribute to very rapid heat conduction in a very short-time regime.