ISSN 1547-4771, Physics of Particles and Nuclei Letters, 2011, Vol. 8, No. 5, pp. 467–469. © Pleiades Publishing, Ltd., 2011. 467 1. INTRODUCTION Research into the spectral properties of atomic radiation in external fields provides important infor- mation about the structure of energy levels and the dynamics of transitions among them. On the other hand, two-level atoms may be considered qubits (information carriers in a quantum computer). This generates a need for a thorough examination of the spectral characteristics of radiation of the interacting atoms in various fields. Traditionally, this kind of problem is solved by using an approach of the quantum theory of open systems [1]. In this case, an assumption about the Markovian character of the interaction of atoms with their envi- ronment, i.e., ignoring the memory effects, is of key importance in deriving kinetic equations. The non- Markovian kinetic equations known from the litera- ture are not free from limitations. The most general Nakashima–Zwanzig equation [2] is more likely of formal interest because it is intractable. Other equa- tions hold good only for a very narrow class of pro- cesses [3] or are phenomenological [4], in which the memory effects are described by introducing addi- tional factors in the Lindblad equation [5]. The aim of this paper is to develop some generali- zation of the Lindblad equation for a system of two dipole–dipole interacting two-level atoms with due regard for processes of interaction with a thermal res- ervoir with short-term memory. The solution to the equation obtained is used to build a contour of the radiation line of a given system and to study its distinc- tion from the line contour calculated in the Markovian approximation. 2. THE MODEL AND KINETIC EQUATION Consider two dipole–dipole interacting two-level atoms in a thermal reservoir. The Hamiltonian of this system is H = H A + H T + H int + H AA + H AF , (1) H A = is the Hamiltonian of free atoms, ω 0 is the frequency of transitions in an atom, and is the diagonal generator of the group SU(2). H T = is the Hamiltonian of a thermo- stat (of a thermal reservoir), ω k is the frequency of the kth photon, and and b k are the kth photon creation and annihilation operators. H int = is the atom– thermostat interaction Hamiltonian, where g kp are the corresponding interaction constants, are increas- ing and reducing atomic operators, R p is the kth atom’s radius vector, and k is a wave vector. H AA = is the dipole–dipole inter- action Hamiltonian and is the dipole–dipole interaction constant. In paper [6], a method is presented for deriving a kinetic equation for the Liouville equation with the initial Hamiltonian for a system of interacting atoms. In a most general case, the kinetic equation can be written as (2) Here, ρ is the atomic density matrix, while is a super operator called the memory kernel. Suppose that the time t'  t, i.e., the time of system observation, is significantly larger than the character- istic memory interval. We can then expand the density matrix under the integral and restrict ourselves only to two terms (3) ћ ω 0 σ p z p ∑ σ p z ћ ω k b k + b k k ∑ b k + ћ g kp b k σ p + e ikRp h.c. + ( ) kp , ∑ σ p ± V pp ' σ p + σ p ' – p p ' ≠ ∑ V pp ' ρ · iH AA ρ t () , [ ] t d ' K ˆ t ' ( )ρ t t ' – ( ) . 0 t ∫ – = K ˆ ρ t t ' – ( ) ρ t () ∂ρ ∂ t ----- t '. – Non-Markovian Relaxation of Atomic Systems and a Calculation of the Shape of Spectral Lines V. V. Semin and A. V. Gorokhov Samara State University, Samara, Russia Abstract—A non-Markovian kinetic equation for a system of two identical interacting two-level atoms has been derived. The solution to this equation has been used for calculating the shape of spectral lines of this system. DOI: 10.1134/S1547477111050165