Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Theory of perturbatively nonlinear quantum transport I: general
  formulation and structure of the retarded correlator   This article is the first of a trilogy that addresses various aspects of the
perturbative response of general quantum systems, with possibly nontrivial
ground state geometry, beyond linear order. Here, we use group theoretical
considerations to investigate the structure of retarded correlators, and
demonstrate how they decompose according to irreducible representations of a
`time-reversal group' and relevant permutation groups, with the former probing
dissipative and time-reversal properties, and the latter discerning
configurational properties -- longitudinal, transverse and their
generalizations. We establish second order fluctuation-dissipation and
fluctuation-reaction theorems, and connect them to well-known second order
transport effects such as the shift and injection currents. Exploiting the
Schur-Weyl duality between irreducible representations of general linear groups
and irreducible representations of permutation groups, we show how to decide
which terms in the decomposition based on the latter can be supported by
different crystals described via the 32 point groups, and perform the full
point group classification for rank 3 and 4 polar and axial tensors. Our
results provide a formal basis for the extraction of uniquely differing
physical effects from retarded correlators. Applications to second order charge
current responses in selected cases are given in part III.

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The categories of this paper are: q-alg
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The categories of this paper are: eess
1
The categories of this paper are: cs
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The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th