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On the absence of stationary currents
Reviews in Mathematical Physics ( IF 1.8 ) Pub Date : 2020-07-13 , DOI: 10.1142/s0129055x20600119
Sven Bachmann 1 , Martin Fraas 2
Affiliation  

We review the 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 dimensions, 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 the many-body charge transport in quantum lattice systems having a conserved [Formula: see text]-charge.

中文翻译:

在没有固定电流的情况下

我们回顾了 Bloch 定理关于量子系统中不存在宏观固定电流的证明。标准证明表明,在相当一般的条件下,一维电流在大体积极限内消失。在更高维度上,横截面的总电流在无间隙系统中不需要消失,但在有间隙系统中确实会消失。我们专注于后一种说法,并给出了一个独立的证明,该证明是由最近引入的具有守恒[公式:见文本]-电荷的量子晶格系统中的多体电荷传输指数推动的。
更新日期:2020-07-13
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