Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topology and Observables of the Non-Hermitian Chern Insulator   Topology plays a central role in nearly all disciplines of physics, yet its
applications have so far been restricted to closed, lossless systems in
thermodynamic equilibrium. Given that many physical systems are open and may
include gain and loss mechanisms, there is an eminent need to reexamine
topology within the context of non-Hermitian theories that describe open, lossy
systems. The recent generalization of the Chern number to non-Hermitian
Hamiltonians initiated this reexamination; however, there is so far no
established connection between a non-Hermitian topological invariant and the
quantization of an observable. In this work, we show that no such relationship
exists between the Chern number of non-Hermitian bands and the quantization of
the Hall conductivity. Using field theoretical techniques, we calculate the
longitudinal and Hall conductivities of a non-Hermitian Hamiltonian with a
finite Chern number to explicitly demonstrate the physics of a non-quantized
Hall conductivity despite an invariable Chern number. These results demonstrate
that the Chern number does not provide a physically meaningful classification
of non-Hermitian Hamiltonians.

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The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
2
The categories of this paper are: math
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The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph