The theory of spin effects (with the particular emphasis on T-odd ones) in QCD and its development in JINR is reviewed, including some personal recollections on the joint work with A.V. Efremov. The analysis of the sources of imaginary phases and respective cuts in hadronic kinematic variables leads to the effective character (non-universality) of T-odd distribution functions, contrary to universality of T-odd fragmentation functions. In particular, the model calculations of DIS with explicit T-violations can be used to predict the oscillations of T-odd polarizing fragmentation function. The comparison of polarization effects in hadronic and heavy-ion collisions is addressed.

The Continuous analogue of Newton's method (CANM), developed at JINR since the 1970s, is one of most important areas of research at Laboratory of Computing Techniques (LCTA) -- Meshcheryakov Laboratory of Information Technologies (MLIT). CANM and its generalization are powerful tools for the effective numerical solution of nonlinear problems within a wide range of complex physical systems studied at JINR. This review article provides a general framework for the CANM-based approach, the main stages in the development and applications of CANM for solving various types of nonlinear problems that have been on the agenda in different years. The results of the development and application of CANM-based iterative methods, obtained over the past 20 years, are presented in more detail. 

We review the results of applying the statistical field-theoretic approach to the problem of fully developed turbulence in nonrelativistic three-dimensional magnetohydrodynamics (MHD), which have been obtained over the past forty years. The review covers both general aspects of the physics of MHD turbulence and the necessary mathematical machinery of statistical field theory, including elements of renormalization theory and the renormalization-group (RG) method. The approach is illustrated using a stochastic model of stationary, locally homogeneous, fully developed three-dimensional MHD turbulence in the general case of a medium with broken spatial parity (helical MHD). In this model, RG techniques make it possible to establish the existence of several infrared-stable scaling regimes and to calculate the critical dimensions of various composite operators, the infrared asymptotics of correlation functions, and the amplitude factors in scaling laws, as well as to incorporate the effects of compressibility, anisotropy, etc.

For an important class of helical MHD systems, the field-theoretic approach provides an elegant formulation of the fundamental problem of large-scale turbulent dynamo action — namely, the generation of a large-scale magnetic field ⟨b⟩ = B (where b denotes magnetic fluctuations) at the expense of the energy of turbulent fluctuations — via the decay of the initial unstable vacuum state ⟨b⟩ = 0 as a result of dynamical spontaneous symmetry breaking in the spirit of the Coleman-Weinberg mechanism, followed by stabilization of the theory in the vicinity of the new ground state ⟨b⟩ = B (the dynamo regime). The field-theoretic formulation we developed, together with a generalization of the standard Feynman diagrammatic technique to the dynamo regime, not only makes it possible to treat within a unified framework the existing theoretical approaches to helical magnetohydrodynamics (kinematic MHD, large-scale dynamo theory), but also extends the RG formalism to the dynamo regime, which — unlike closure procedures still common in dynamo theory — is particularly well suited for studying statistically stationary turbulent states. The richness of MHD physics in the dynamo regime is illustrated both in the emergence of new effects (Goldstone-type corrections to Alfvén waves, anisotropic corrections associated with the transport of the large-scale field) and in the theoretically predicted strong dependence of the magnetic energy-spectrum slope on the degree of mirror-symmetry breaking.

We construct superconformal mechanics with N = 3 and N = 4 supersymmetries that were inspired by analogy with the supersymmetric Schwarzian mechanics. The Schwarzian, being another system with superconformal symmetry, provides insight into the field content of supersymmetric mechanics, most notably, on the number and properties of the fermionic fields involved. Adding more fermionic fields (four in the N = 3 case and eight in the N = 4 case) made it possible to construct systems possessing maximal superconformal symmetries in N = 3 and N = 4, namely osp(3|2) and D(1, 2; α). In the case of N = 4 supersymmetry, we explicitly construct a new variant of N = 4 superconformal mechanics in which all bosonic subalgebras of the D(1, 2; α) superalgebra have a bosonic realization. In addition, the constructed systems involve the so(3) currents whose parameterization is not fixed, which allows one to consider different underlying geometries.

This short review is devoted to the celebration of two major events in quantum physics. The first one is the birth of the concept of Bose–Einstein condensation (1925) and the second is the experimental proof that it does exist and appears in liquid ⁴He simultaneously with superfluidity below the λ-point (1975).
Both of these events are tightly related to the Bogoliubov theory of superfluidity (1947). The existence of condensate in the system of interacting bosons is the key ansatz of this theory. Therefore, the experiments started at JINR-Dubna in 1975 confirmed this prediction of the Bogoliubov theory that superfluidity of liquid ⁴He (He II) should emerge at the same time as the Bose–Einstein condensation.

Corrected:
13 November 2025 (the captions to Figures 1 and 2 were changed)
26 November 2025 (changes were made in formulas (53) and (55))

We consider a complex rational degeneration of the hyperbolic Ruijsenaars model emerging in the limit ω₁ + ω₂ → 0 (or b → i in 2d CFT) and investigate the two-particle case in detail. Corresponding wave functions are described by complex hypergeometric functions in the Mellin–Barnes representation. Their dual integral representation and reflection symmetry in the coupling constant are established. Besides, a complex limit of the hyperbolic Baxter Q-operators is considered. Another complex degeneration of the hyperbolic Ruijsenaars model is obtained by taking a special ω₁ − ω₂ → 0 (or b → 1) limit. Additionally, two new degenerations to the complex Calogero–Sutherland type models are described.