Quantum Transport in a Crystal with Short-Range Interactions: The Boltzmann-Grad Limit
Quantum Transport in a Crystal with Short-Range Interactions: The Boltzmann-Grad Limit
复制标题
具有短程相互作用的晶体中的量子输运：玻尔兹曼梯度极限
DOI：
10.1007/s10955-021-02797-z
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发表时间：
2021
影响因子：
1.6
通讯作者：
Griffin J
中科院分区：
文献类型：
--
作者：
Griffin J
研究了具有短程势的晶体中量子洛伦兹气体的宏观输运性质，证明了在Boltzmann-Grad极限下量子动力学收敛于与线性Boltzmann方程不相容的随机飞行过程.我们的推导依赖于一个关于薄域中格点统计分布的假设，这与量子混沌中的Berry-Tabor猜想密切相关。
We study the macroscopic transport properties of the quantum Lorentz gas in a crystal with short-range potentials, and show that in the Boltzmann–Grad limit the quantum dynamics converges to a random flight process which is not compatible with the linear Boltzmann equation. Our derivation relies on a hypothesis concerning the statistical distribution of lattice points in thin domains, which is closely related to the Berry–Tabor conjecture in quantum chaos.