### Article

## Plasma-Plasma and Liquid-Liquid First-Order Phase Transitions

Ab initio quantum modeling is applied to check the ideas that motivated studies of both plasma phase transition (PPT) and Brazhkin semiconductor-to-metal phase transition, and to analyze both similarity and difference between them as well as with the Wigner metallization. Electron density of states and the characteristic gap in it are investigated to verify the semiconductor-to-metal nature of the transition. The change of plasma frequency is suggested to be used instead of the “degree of ionization” to characterize the difference between two plasma phases at PPT. Electron density of states, pair distribution function, and conductivity are calculated as well. It is shown that Norman-Starostin ideas about (a) PPT and (b) phase diagram for fluids are not anymore a hypothesis. They are confirmed by the experimental data.

Warm dense matter (WDM) is a state of a substance with a solid-state density and temperature from 1 to 100 eV. Researchers believe that such a state exists in the cores of giant planets. Investigation of WDM is important for some applications, such as surface treatment on the nanometer scale, laser ablation, and the formation of the plasma sources of the X-ray radiation into the inertial synthesis. In this study, the conductivity and the thermal conductivity are calculated based on density functional theory and the Kubo-Greenwood theory. This approach was already used to simulate the transport properties in a broad range of densities and temperatures, and its efficiency has been demonstrated. The conductivity and the thermal conductivity of aluminum and gold are investigated. Both the isothermal state, when the electron temperature equals the ion temperature, and the two-temperature state, when the electron temperature exceeds the ion temperature, are considered. The calculations were performed for a solid body and liquid in the range of electron temperatures from 0 to 6 eV.

Warm dense matter conductivity and reflectivity are investigated by means of density functional theory. Both one- and two-temperature cases are considered. One-temperature mode is related to equilibrium state where temperature of electrons and ions are equal. As an example of one-temperature system xenon plasma is studied. The reflectivity of shock-compressed dense xenon plasma is calculated and compared with experimental data. Two-temperature mode is associated with different temperature of electrons and ions. The thermal conductivity of aluminum and gold in such mode is examined. The comparison of obtained results with theoretical model based on Boltzmann equation is conducted.

Non-equilibrium two-temperature warm dense metals consist of the ion subsystem that is subjected to structural transitions and involved in the mass transfer, and the electron subsystem that in various pulsed experiments absorbs energy and then evolves together with ions to equilibrium. Definition of pressure in such non-equilibrium systems causes certain controversy. In this work we make an attempt to clarify this definition that is vital for proper description of the whole relaxation process. Using the density functional theory we analyze on examples of Al and Au electronic pressure components in warm dense metals. Appealing to the Fermi gas model we elucidate a way to find a number of free delocalized electrons in warm dense metals.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.