¹Samara State University, Samara, Russia
²Institute of Mathematical Problems of Biology RAS –the Branch of Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Pushchino, Russia
³Bogoliubov Laboratory of Theоretical Physics, JINR, Dubna, Russia
⁴Dubna State University, Dubna, Russia

Abstract. The quantum-statistical model proposed earlier by Skourtis and Nitzan to describe a charge (hole) propagation in a fragment of artificial DNA molecule has been generalized and further investigated.  A numerical simulation of a charge transport was carried out taking into account two different dissipative processes, including the capture of the charged carrier by the environment and the decoherence of its quantum wave properties due to the influence of stochastic fields of the environment. The interaction of the carrier with the environment is regulated by a small set of phenomenological parameters whose values vary in the process of   simulation. Within this model, the propagation of a hole carrier in DNA is described by solving the quantum Franke-Kossakovski–Lindblad–Glauber–Sudarshan equation (hereinafter referred to as the Lindblad equation) for the carrier density matrix using the Lindblad MPO Solver program. Results of numerical analysis of the model are in a good agreement with experimental observations and demonstrate two different types of the charged carrier motion, presumably tunneling and incoherent hopping. The model is put in more general context and non-unitary dynamics of the hole carrier is treated within the framework of a theory of continuous quantum measurements by the environment in an open quantum system. The main concepts of the theory of decoherence and superselection for open quantum systems and the prospects for their application for further study of various mechanisms of motion of a charged carrier in DNA are briefly discussed.

Key words: electronic structure of DNA, modeling of charge transfer in DNA, open quantum systems, Lindblad equation.