In this work, we study the case, in which the distances between atoms are quite large, so that the average distances between atoms are greater or in the same order than the

‘resonant transition’ wavelength. Therefore, we prepare an ensemble of N two-level atoms initially in ground state, Proteasome inhibitors in cancer therapy and a single mode of the radiation field is excited in a ‘Fock’ state (so called one-photon state). This is the case of a purely monochromatic wave with zero line width under the consideration. A laser output in single mode operation can approximate this situation due to its high degree of monochromaticity (small line width) for instance. The mode of electromagnetic field is specified completely by giving its wave vectors k 0 with atomic transition frequency ω = c|k 0| and its polarization j (j = 1, 2). The main feature, differentiating our research from others in this domain, is the developed direct and consistent solution to the N-particle equations, describing the time evolution of the N atomic probability state amplitudes. Besides, in certain sense, we explained the nature of the widely used Weisskopf-Wigner approximation that was not found in the reviewed by us scientific

literature. The goal of this paper can be formulated as an attempt to propose an adapted and simple in practical use theory, for example in the highly applied nanoscale physics. The proposed theoretical material requires corresponding RG-7388 molecular weight experimental verification. As an idea of an application, the model system can be realized on atomic (developing the method proposed in [1] for the nuclei of 57Fe in certain composites, but this time for a visible region), chains of trapped ions (like in [8]), and molecular structures for further developing such techniques like FRET (described for instance in [12]), atomic chains like carbyne loops (for example, [13]), and microhole array synthesized by femtosecond laser radiation (see [14], for an instance). Let us first provide below some general theoretical premises. More detailed derivations of the corresponding

mathematical model Adenosine triphosphate can be found in [11]. Methods The equations of motion for the state GDC-0068 clinical trial amplitudes We have assumed that the atomic energy levels have no linewidth, so that, only if , the atoms can be able to absorb a photon. Obviously, this is an unrealistic case since it is impossible to have a completely monochromatic wave. In addition, for the case of the Fock initial state, in which we measured the energy precisely of the mode, the average electric field will be zero. In the forth of the law of energy conservation, an emitted photon will correspond to the same frequency (we can say it will occur with a high probability after a quite long time interval if the system has a damping). Therefore, consider a collection of N identical atoms, at positions r 1,…,r α ,…,r N , coupled to a one mode electromagnetic (EM) field. Each atom α = 1..