Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Open quantum random walks, hitting times, gambler's ruin and potential
  theory   We consider a model of open quantum random walk and together with a quantum
trajectory approach we are able to examine a notion of hitting time. We see
that many constructions, such as minimal solutions to hitting time problems,
are variations of well-known classical probability results, but the density
matrix degree of freedom on each site gives rise to systems which are seen to
be nonclassical. As a more specific application we study the collection of
walks induced by normal commuting contractions, for which the corresponding
probability expressions are obtained. We examine quantum versions of the
gambler's ruin, birth-and-death chain and a basic theorem on potential theory.

13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin