Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the absence of stationary currents   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.

37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph