Research / Main fundamental results / Non-equilibrium processes and transport phenomena

# Non-equilibrium processes and transport phenomena

The studies of non-equilibrium processes and transport phenomena in condensed matter systems were founded in 1980 by initiative of academician Prof. I. R. Yukhnovskii. At that time they concerned the problems of inverse osmotic transport processes in aqueous solutions through porous media and the calculations of time correlation functions and transport coefficients for electrolyte solutions. Further directions of investigations of nonequilibrium processes were formed in close collaboration with Prof. D. N. Zubarev (Steklov Institute of Mathematics of the Russian Academy of Sciences). As a result, a whole areas of study of non-equilibrium processes and transport phenomena in dense gases, plasma, polar and magnetic fluids, as well as in electrolyte solutions has been emerged (M.V. Tokarchuk, I. M. Mryglod, I. P. Omelyan, T. M. Bryk).

**Theory of kinetic and hydrodynamic processes.** On the basis of the non-equilibrium statistical operator by D. N. Zubarev the concept of a self-consistent description of kinetic and hydrodynamics processes in dense gases, liquids and their mixtures was proposed. As a result, the cluster expansions to the hierarchy of the BBGKY equations for non-equilibrium particle distribution functions have been obtained. The kinetic equation of the revised Enskog theory was consequently derived in the pair-collision approximation for a system of hard spheres for the first time. The generalized Enskog equation for a model of hard spheres and the kinetic equation by Bogolyubov, Lennard and Balescu have been derived as well. The kinetic equation for a system of interacting particles with many-step potentials has been proposed and the H-theorem has been proven. A concept of a self-consistent description of kinetic and hydrodynamic processes for dense plasma in internal electromagnetic field with taking into account the kinetics of photons was developed. The generalized equations with the transport coefficients, such as viscosity, conductivity and self-diffusion, which take into account the inhomogeneity of photon filed, has also been obtained.

For classical liquids on the basis of the proposed concept a system of coupled equations for the non-equilibrium one-particle distribution function and averaged value of potential energy of interaction, which for weakly non-equilibrium processes give the possibility to investigate of collective excitations, time correlation functions and generalized transport coefficients for intermediate values of wave-vector and frequency was derived. The existence of kinetic modes in the long wavelength limit has been proven as well.

**In the generalized hydrodynamics theory of liquids**, the original approach, namely, the method of generalized collective modes, which allows one within the framework of unique formalism to study spectra of generalized collective excitations, time correlation functions, as well as wave-vector and frequency dependent transport coefficients in dense liquids and mixtures has been proposed. The method was formulated in a computer-adapted form, which is free of any adjustable parameters and thus is convenient for combining of analytical theory and computer experiment. The formalism of generalized collective modes was used for the investigation of dynamics of simple, semi-quantum and magnetic fluids, liquid metals and their alloys, as well as binary and multi-component mixtures. The numerical results were obtained in a wide region of varying of wave-vector and frequency (from the hydrodynamic regime up to limiting Gaussian behavior). They transparently demonstrate a good agreement with computer simulation data. Among a whole set of new results it is worth emphasizing the following: the clarifying of the mechanism of appearance of shear waves and excitations like “heat wave” in simple fluids and their mixtures; the explanation of the origin of the phenomena of type “fast sound” in binary mixtures with large difference in masses of particles and in fluids, where quantum effects are important; the obtaining of analytical solutions for dynamical structure factors of magnetic fluids and many-component mixtures in the hydrodynamic region.

**In the dynamical theory of molecular fluids**, the method of generalized collective modes for the study of longitudinal dynamical fluctuations was developed. Analytical expressions were obtained for time correlation functions and generalized transport coefficients related to fluctuations of the number of particles, momentum and energy with taking into account of spatial distributions of atoms within the molecule. The proposed approach has been applied to the description of dynamical processes in water on the basis of the TIP4P model. The molecular dynamics simulations have been carried out for this model as well. On the basis of comparison of the obtained theoretical results with the computer experiment data it has been shown that the explicit account of non-markovian effects in the kinetic memory kernels gives the possibility to calculate not only qualitatively but also quantitatively the bulk viscosity, conductivity and dynamical structure factor in the whole region of frequencies and wave-vectors using only several generalized collective modes. It has been demonstrated that the taking into account explicitly the atomic structure of molecules is important in the region of intermediate and large values of wave-vector as well as in the long wavelength limit.

**In the theory of dynamical properties of spin liquids**, a new approach has been proposed for the integration of the equations of motion in computer experiment. It is based on the formalism of Liouville operators in conjunction with the application of the factorization of exponential propagators. This allows one to perform the calculation of dynamical structure factors like spin-spin, spin-density, and density-density for the Heisenberg model. The possibility of propagation of longitudinal spin waves in magnetic liquids at sound frequency has been established. This should be considered as a new effect, which can be observed experimentally.

**In the theory of quantum liquids**, the investigations of dynamical properties of semi-quantum helium Не-4 have been carried out in the quasi-hydrodynamic region. The equations of generalized hydrodynamics have been obtained and the spectrum of collective excitations has been analyzed in the region of small and intermediate values of wave-vector. The calculations of the dynamical structure factor and other correlation functions were performed at temperatures 4 К and 8 К with the extraction of partial contributions of each collective mode. As is shown, the appearance of experimentally observed plateaux in the dynamical structure factor is well described within the proposed model. The calculation of spatial-time dispersion of the transport coefficients is carried out too.

The approach **of the consistent description of kinetics and hydrodynamics in many-boson systems** has also been developed. The generalized transport equations have been constructed for strongly- and weakly-correlated Bose-systems with the help of the method of the non-equilibrium statistical operator. The generalized transport equations were obtained with taking into account the consistent description of kinetic and hydrodynamic processes.

The **non-equilibrium thermo-field dynamics** for the first time on the basis of the non-equilibrium statistical operator method by Zubarev for the description of quantum-field systems has been formulated. The generalized transport equations of the self-consistent description of kinetic and hydrodynamic processes were obtained in thermo-field representation. Such equations have been applied to a quark-gluon plasma.