论文标题
具有非平凡量子几何形状和物理量的期望值的系统的半古典动力学理论
Semiclassical kinetic theory for systems with non-trivial quantum geometry and the expectation value of physical quantities
论文作者
论文摘要
从Keldysh理论开始，对于一般的低能$ n $ band hamiltonian，我们在干净的限制下进行了明显的$ \ smash {u（1）\ times \ times su（n）} $量表不变性的半经典扩展。显示出广泛的浆果曲率张量可以控制光谱重量的重新分布。随之而来的是某些物理数量的新表达式，建立了先前提出的对状态密度的校正的限制。在两种频段的情况下，我们得出了一个完全通用的半经典动力学理论，包括所有$ o（\ hbar）$量子校正。作为一种应用，我们在所有通用性中都展示了如何通过单个简单的计算，手性异常，内在的异常电导率和手性磁效应来恢复。我们的形式主义的灵活性和效率源于量子动力学的潜在复杂性所提供的绝缘材料，尽管它与更深层次的水平进行了严格的联系。
Starting from the Keldysh theory, for a general low energy $N$-band Hamiltonian in the clean limit, we perform a manifestly $\smash{U(1) \times SU(N)}$ gauge invariant semiclassical expansion. A generalized Berry curvature tensor is shown to control a redistribution of spectral weights. New expressions for certain physical quantities ensue, establishing the limits of a previously proposed correction to the density of states. In the two-band case, we derive a completely general semiclassical kinetic theory including all $O(\hbar)$ quantum corrections. As an application, we show how one can recover, out of a single simple calculation, the chiral anomaly, intrinsic anomalous Hall conductivity and chiral magnetic effect, in all generality. The demonstrated flexibility and efficiency of our formalism derives from the insulation it provides from the underlying complexity of the quantum kinetics, notwithstanding its rigorous connection to this deeper level.
