Site recurrence for continuous-time open quantum walks on the line

In recent years, several properties and recurrence criteria of discrete-time open quantum walks (OQWs) have been presented. Recently, Pellegrini introduced continuous-time (CTOQWs) as natural limits OQWs. this work, we study semifinite CTOQWs some their basic concerning statistics, such transition probabilities site recurrence. The notion SJK-recurrence for is introduced, it shown to be equivalent the traditional concept This statistic arises from definition $\delta$-skeleton CTOQWs, which a dynamic that allows us obtain OQW in terms CTOQW. We present complete criterion case CTOQW induced by coin finite dimension with set vertices $\mathbb{Z}$ its auxiliary Lindblad operator has single stationary state. Finally, similar completes internal degree freedom each 2.