Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From operator statistics to wormholes   For a generic quantum many-body system, the quantum ergodic regime is defined
as the limit in which the spectrum of the system resembles that of a random
matrix theory (RMT) in the corresponding symmetry class. In this paper we
analyse the time dependence of correlation functions of operators. We study
them in the ergodic limit as well as their approach to the ergodic limit which
is controlled by non-universal massive modes. An effective field theory (EFT)
corresponding to the causal symmetry and its breaking describes the ergodic
phase. We demonstrate that the resulting Goldstone-mode theory has a
topological expansion, analogous to the one described in arXiv:2008.02271 with
added operator sources, whose leading non-trivial topologies give rise to the
universal ramp seen in correlation functions. The ergodic behaviour of
operators in our EFT is seen to result from a combination of RMT-like spectral
statistics and Haar averaging over wave-functions. Furthermore we analytically
capture the plateau behaviour by taking into account the contribution of a
second saddle point. Our main interest are quantum many-body systems with
holographic duals and we explicitly establish the validity of the EFT
description in the SYK-class of models, starting from their microscopic
description. By studying the tower of massive modes above the Goldstone sector
we get a detailed understanding of how the ergodic EFT phase is approached and
derive the relevant Thouless time scales. We point out that the topological
expansion can be reinterpreted in terms of contributions of bulk wormholes and
baby-universes.

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The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg