For the system with one-dimensional spatially periodic potential we demonstrate that small periodic in time perturbation results in appearance of chaotic instanton solutions. We estimate parameter of local instability, width of stochastic layer and correlator for perturbed instanton solutions. Application of the instanton technique enables to calculate the amplitude of the tunneling, the form of the spectrum and the lower bound for width of the ground quasi-energy zone.

Over 30 years there has been no comprehensive understanding of the mechanism of soft photons (energy smaller than 50 MeV) formation. Experimental data indicate an excess of their yield in hadron and nuclear interactions in comparison with calculations performed in QED. For a more thorough study of this phenomenon at the Nuclotron (a superconducting accelerator in JINR), preliminary measurements have been carried out with using an electromagnetic calorimeter based on BGO crystals. These results are consistent with the world data. In JINR, in connection with the building of a future accelerator complex NICA, it has become possible to carry out such studies in pp, pA and AA interactions at energies up to 25 A GeV. Our group develops the conception of an heterogeneous electromagnetic calorimeter as “spaghetti” and “shashlik” types based on gadolinium gallium garnet (GaGG) crystals with a low threshold for registration of photons. The first tests of prototypes of them manufactured at JINR on the basis of the GaGG and a mixture of tungstate and copper as an absorber are reported.

In the framework of the diagrammatic approach, the total cross section of near-threshold π– photoproduction on the deuteron is calculated. Contributions of the diagrams corresponding to the plane wave impulse approximation as well as to NN- and πN-interactions in the final state have been taken into account. We have compared the theoretical predictions with the results of the recent measurements performed at the MAX IV laboratory of the Lund University. There is good agreement with the data at photon energies from 147 to 155 MeV. However, at 158 and 160 MeV, the theoretical predictions significantly overestimate the measured cross sections.

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More than ten-year experimental search for collective phenomena in high multiplicity events has been carried out at the Laboratory of high energy physics at JINR. We present main results, which have been received at the U-70 accelerator (IHEP, Protvino) in the proton collisions and at Nuclotron ( JINR, Dubna) in the nuclear interactions. For interactions, topological cross sections have been gone three orders down and achieved KNO-scaling variable ( / ) 4.5. Probably, the tail of high multiplicity distribution stipulates gluon splitting. In the region of high multiplicity, the formation of pions is predominant. Some collective phenomena are predicted in this region. Using charged multiplicity data, we could restore total (sum of charged and neutral particles) multiplicity and have implemented unique research for fluctuations of the neutral particle number at the given total multiplicity. The revealed growth of scaled variance may indicate the pion (Bose-Einstein) condensate formation. The excess of soft photon yield at interactions of the Nuclotron beams (d, Li and C) with a carbon target has been confirmed. This can be connected with the pion condensate formation. Currently, we prepare two-shoulder electromagnetic calorimeter to carry out experimental studies at BM@N setup and plan to take part in new experiments on heavy ion collisions at Nuclotron.