Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chaos, Complexity, and Random Matrices   Chaos and complexity entail an entropic and computational obstruction to
describing a system, and thus are intrinsically difficult to characterize. In
this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE)
Hamiltonians and analytically compute out-of-time-ordered correlation functions
(OTOCs) and frame potentials to quantify scrambling, Haar-randomness, and
circuit complexity. While our random matrix analysis gives a qualitatively
correct prediction of the late-time behavior of chaotic systems, we find
unphysical behavior at early times including an $\mathcal{O}(1)$ scrambling
time and the apparent breakdown of spatial and temporal locality. The salient
feature of GUE Hamiltonians which gives us computational traction is the
Haar-invariance of the ensemble, meaning that the ensemble-averaged dynamics
look the same in any basis. Motivated by this property of the GUE, we introduce
$k$-invariance as a precise definition of what it means for the dynamics of a
quantum system to be described by random matrix theory. We envision that the
dynamical onset of approximate $k$-invariance will be a useful tool for
capturing the transition from early-time chaos, as seen by OTOCs, to late-time
chaos, as seen by random matrix theory.

28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph