This is a study of cooperative interaction of radiators with a thermal electromagnetic field and with a single-mode cavity field. It was investigated the interaction between the quantized cavity field and atomic string consisting of equidistant three-level atoms which is injected at such a low flux that at most one atom at a time is present inside the cavity. The trapping conditions for the flying time in a cavity are obtained. Moreover, it was received the so called cotangent state for the proposed systems. The properties of cavity fields are examined. In various limits, the state exhibits vacuum nutation as well as sub-Poissonian statistics and squeezing properties. The spontaneous emission of a multilevel equidistant excited quantum oscillator in case when the symmetry of the dynamical transitions between the levels is submitted to the SU(1,1) symmetry group is studied and compared with those well-known for the SU(2) symmetry. The cooperative generation of phonon pulses in chalcogenide glasses by groups of inverted equidistant multilevel coupled excitations (electrons, excitons) is investigated. Such equidistant systems take place in chalcogenide glasses with fractal structure.