Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operator complexity: a journey to the edge of Krylov space   Heisenberg time evolution under a chaotic many-body Hamiltonian $H$
transforms an initially simple operator into an increasingly complex one, as it
spreads over Hilbert space. Krylov complexity, or `K-complexity', quantifies
this growth with respect to a special basis, generated by $H$ by successive
nested commutators with the operator. In this work we study the evolution of
K-complexity in finite-entropy systems for time scales greater than the
scrambling time $t_s>\log (S)$. We prove rigorous bounds on K-complexity as
well as the associated Lanczos sequence and, using refined parallelized
algorithms, we undertake a detailed numerical study of these quantities in the
SYK$_4$ model, which is maximally chaotic, and compare the results with the
SYK$_2$ model, which is integrable. While the former saturates the bound, the
latter stays exponentially below it. We discuss to what extent this is a
generic feature distinguishing between chaotic vs. integrable systems.

29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
2
The categories of this paper are: math
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph