Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Divisibility hierarchy of open quantum systems   In the theory of open quantum systems, divisibility of the system dynamical
maps is related to memory effects in the dynamics. By decomposing the system
Hilbert space as a direct sum of several Hilbert spaces, we study the
relationship among the corresponding dynamical maps. It is shown that if the
dynamical maps of the open system possess a chain of invariant subspaces, there
exists a divisibility hierarchy for their corresponding dynamics. Two classes
of examples are given for illustrating these hierarchical structures. One is
the pure-dephasing dynamics, and the other is the decay dynamics. Our results
offer a systematic approach to obtaining the divisibility conditions and
non-Markovian witnesses for these dynamics. Moreover, as a new way of
decomposing open quantum systems, it is worthy of further study.

27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex