We consider independent electrons in a periodic crystal in their ground state, and turn on a uniform electric field at some prescribed time. We rigorously define the current per unit volume and study its properties using both linear response and adiabatic theory. Our results provide a unified framework for various phenomena such as the quantization of Hall conductivity of insulators with broken time-reversibility, the ballistic regime of electrons in metals, Bloch oscillations in the long-time response of metals, and the static conductivity of graphene. We identify explicitly the regime in which each holds.

中文翻译：

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周期晶体中的相干电子传输

我们认为周期晶体中处于基态的独立电子会在规定的时间开启均匀的电场。我们严格定义每单位体积的电流，并使用线性响应和绝热理论研究其特性。我们的结果为各种现象提供了一个统一的框架，例如量化具有可逆时间破坏性的绝缘子的霍尔电导率，金属中电子的弹道形式，金属长期响应中的布洛赫振荡以及石墨烯的静态电导率。我们明确确定了各自所处的政权。