Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Markovianity and memory effects in quantum open systems   Although a number of measures for quantum non-Markovianity have been proposed
recently, it is still an open question whether these measures directly
characterize the memory effect of the environment, i.e., the dependence of a
quantum state on its past in a time evolution. In this paper, we present a
criterion and propose a measure for non-Markovianity with clear physical
interpretations of the memory effect. The non-Markovianity is defined by the
inequality $T(t_2,t_0)\neq T(t_2,t_1)T(t_1,t_0)$ in terms of memoryless
dynamical map $T$ introduced in this paper. This definition is conceptually
distinct from that based on divisibility used by Rivas et al (Phys. Rev. Lett
105, 050403 (2010)), whose violation is manifested by non-complete positivity
of the dynamical map. We demonstrate via a typical quantum process that without
Markovian approximation, nonzero memory effects (non-Markovianity) always exist
even if the non-Markovianity is zero by the other non-Marovianity measures.

33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio