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.

中文翻译：

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具有短程相互作用的晶体中的量子输运：Boltzmann-Grad 极限

我们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，并表明在玻尔兹曼-格拉德极限下，量子动力学收敛到与线性玻尔兹曼方程不兼容的随机飞行过程。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。