Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diffusive-to-ballistic crossover of symmetry violation in open many-body
  systems   Conservation laws in a quantum many-body system play a direct role in its
dynamic behavior. Understanding the effect of weakly breaking a conservation
law due to coherent and incoherent errors is thus crucial, e.g., in the
realization of reliable quantum simulators. In this work, we perform exact
numerics and time-dependent perturbation theory to study the dynamics of
\textit{symmetry violation} in quantum many-body systems with slight coherent
(at strength $\lambda$) or incoherent (at strength $\gamma$) breaking of their
local and global symmetries. We rigorously prove the symmetry violation to be a
divergence measure in Hilbert space. Based on this, we show that symmetry
breaking generically leads to a crossover in the divergence growth from
diffusive behavior at onset times to ballistic or hyperballistic scaling at
intermediate times, before diffusion dominates at long times. More precisely,
we show that for local errors the leading coherent contribution to the symmetry
violation cannot be of order lower than $\propto\lambda t^2$ while its
leading-order incoherent counterpart is typically of order $\propto\gamma t$.
This remarkable interplay between unitary and incoherent gauge-breaking
scalings is also observed at higher orders in projectors onto symmetry
(super)sectors. Due to its occurrence at short times, the
diffusive-to-ballistic crossover is expected to be readily accessible in modern
ultracold-atom and NISQ-device experiments.

17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th