论文标题
在没有固定电流的情况下
On the absence of stationary currents
论文作者
论文摘要
我们回顾了Bloch定理的证据，内容涉及量子系统中没有宏观固定电流。标准证明表明，在相当普遍的条件下，1D的电流在较大的体积限制下消失。在较高的维度中，横截面上的总电流不需要在无间隙系统中消失，但在间隙系统中确实消失了。我们专注于后者的主张，并给出一个独立的证据，该证明是由最近引入的索引，用于具有保守的$ U（1）$ - 收费的量子晶格系统中的多体电荷运输。
We review proofs of a theorem of Bloch on the absence of macroscopic stationary currents in quantum systems. The standard proof shows that the current in 1D vanishes in the large volume limit under rather general conditions. In higher dimension, the total current across a cross-section does not need to vanish in gapless systems but it does vanish in gapped systems. We focus on the latter claim and give a self-contained proof motivated by a recently introduced index for many-body charge transport in quantum lattice systems having a conserved $U(1)$-charge.
