It is proposed a new approach in the estimation of quantum fluctuations of the electromagnetic field and Doppler effect using a model formed from two quantum modes of the cavity which propagate in opposite direction. The Doppler effect plays a significant role in the model in which an atom flies through the nodes and anti-nodes of the standing wave. It is shown that if the vacuum Rabi frequency achieves the value of Doppler shift <i>kv</i>, where <i>k</i> is the wave vector and <i>v</i> represents the atomic velocity, then the collective interactive and non-interactive modes of the resonator become connected. The interaction process looks like in the case of two coupled cavities in one of which is placed an atom. The comparison between the proposed approach and existing time dependent coupling model is given. In our model, it is obtained the non-zero value of quantum fluctuations in the nodes of the standing wave during the time in which atom flies through the cavity.
The resonance fluorescence of an atomic (or ion) system implanted in the materials driving two standing waves of the optical cavity is studied taking into consideration the delocalization of the atom. It is demonstrated that the resonance fluorescence depends on the position of atoms (or ions) relative the nodes or antinodes of standing waves. This situation gives us the possibility to measure the amplitude of mechanical oscillations of these radiators implanted in organic or inorganic materials. It is proposed to measure the amplitude of the mechanical oscillations relative to the equilibrium position using the time changes in the positions of the five peaks of the resonance fluorescence spectrum. In this case, the small oscillation amplitude relative to the standing wave length can drastically change the spectrum of resonance fluorescence of such atoms. The proposed method can be used in the measurements of the nanostructure temperature (or bio-molecule temperature deformation).
Taking into consideration the granulate glass deposition of the <i>TiO</i><sub>2</sub> glass we propose a phenomenological model describing the nonlinear process of the growth of <i>Ti</i> and <i>TiO</i><sub>2 </sub>films on <i>Si </i>or <i>SiO</i><sub>2</sub> substrates as function of temperature. It is proposed that the phase transition can take place in earth granule so that the fixed Tg temperature is absent in comparison with traditional phase transition from thermodynamics. The continue temperature transition from crystalline to vitreous phase in the deposited films is analyzed based upon the nonlinear theory of phase transitions and the granulate aspect of deposited material.