Coexistence of the "bogolons" and the one-particle spectrum of excitations with a gap in the degenerated Bose gas

Properties of the weakly non-ideal Bose gas are considered without suggestion on C-number representation of the creation and annihilation operators with zero momentum. The "density-density" correlation function and the one-particle Green function of the degenerated Bose gas are calculated on the basis of the self-consistent Hartree-Fock approximation. It is shown that the spectrum of the one-particle excitations possesses a gap whose value is connected with the density of particles in the "condensate". At the same time, the pole in the "density-density" Green function determines the phonon-roton spectrum of excitations which exactly coincides with one discovered by Bogolyubov for the collective excitations (the "bogolons").Comment: 8 pages, no figure

Research of the thermal desorption processes in oxide mixtures at laser effect

To investigate the physical-chemical processes occurring during the heating stage of spent nuclear fuel magneto plasma reprocessing a study of thermal desorption of oxides and oxide mixtures as SNF simulators under the influence of stationary laser radiation are being studied. Preliminary experiments were carried out. X-ray diffraction and energy dispersive X-ray microanalysis of the film deposited on the substrate after laser influence on a mixture of B₂O₃/ZrO₂ oxides have been performed.Для вивчення фізико-хімічних процесів, що відбуваються на стадії нагріву магнітоплазмової переробки відпрацьованого ядерного палива (ВЯП), проводиться дослідження процесів термодесорбції оксидів і оксидних сумішей - імітаторів ВЯП при впливі стаціонарного лазерного випромінювання. Проведено попередні експерименти, виконані рентгенодифракційний і енергодисперсійний рентгенівський мікроаналізи плівки, осадженої на підкладку після лазерного впливу на суміш оксидів B₂O₃/ZrO₂.Для изучения физико-химических процессов, происходящих на стадии нагрева магнитоплазменной переработки отработавшего ядерного топлива (ОЯТ), проводится исследование термодесорбции оксидов и оксидных смесей – имитаторов ОЯТ при воздействии стационарного лазерного излучения. Проведены предварительные эксперименты, выполнены рентгенодифракционный и энергодисперсионный рентгеновский микроанализы пленки, осажденной на подложку при лазерном воздействии на смесь оксидов B₂O₃/ZrO₂

Lifetime distributions in the methods of non-equilibrium statistical operator and superstatistics

A family of non-equilibrium statistical operators is introduced which differ by the system age distribution over which the quasi-equilibrium (relevant) distribution is averaged. To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. Superstatistics, introduced in works of Beck and Cohen [Physica A \textbf{322}, (2003), 267] as fluctuating quantities of intensive thermodynamical parameters, are obtained from the statistical distribution of lifetime (random time to the system degeneracy) considered as a thermodynamical parameter. It is suggested to set the mixing distribution of the fluctuating parameter in the superstatistics theory in the form of the piecewise continuous functions. The distribution of lifetime in such systems has different form on the different stages of evolution of the system. The account of the past stages of the evolution of a system can have a substantial impact on the non-equilibrium behaviour of the system in a present time moment.Comment: 18 page

The problem of the universal density functional and the density matrix functional theory

The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation

The problem of the universal density functional and the density matrix functional theory

The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation

External field as the functional of inhomogeneous density and the density matrix functional approach

Based on the Hohenberg-Kohn lemma and the hypotheses of the density functional existence for the external-field potential, it is shown that the strict result of the density functional theory is the equation of the external-field potential as the density functional. This result leads to the impossibility of determining the inhomogeneous density in a given external field if the inhomogeneous density is not known a priori. The problem encountered is intimately associated with the absence of a regular procedure for determining the universal density functional. The result obtained shows the advantage of the density matrix functional theory which yields a correct description of the inhomogeneous electron system in both the ideal-gas approximation and the self-consistent Hartree-Fock approximation in contrast to the density functional theory. Copyright (C) EPLA, 201

Reply to the Comment by D. P. Joubert

no abstrac

Exact relation in the density functional body

Based on the Hohenberg-Kohn theorem, an exact integral expression is derived, which relates the nonuniform density to the inverse response function in the equilibrium system of interacting electrons. This relation is a necessary condition for the existence of the universal density functional in the density functional theory. The possibility of developing a regular procedure for calculating the density functional for the free energy or ground-state energy is shown

Effective pair potential for atoms in the Coulomb model of substance

An explicit expression for the pair short-range effective interaction potential of "atoms" is derived based on the model of "pure" matter. This model represents the equilibrium Coulomb system of interacting electrons and nuclei of the same type, using the adiabatic approximation for nuclei, the self-consistent Hartree-Fock approximation for the electronic subsystem, the "one-center" approximation to describe localized electronic states, and the perturbation theory with respect to the fluctuating field. It is shown that the found potential is completely defined by the inhomogeneous density and inhomogeneous density matrix of electronic states in the isolated "atom"

Effective pair potential for atoms in the Coulomb model of substance

An explicit expression for the pair short-range effective interaction potential of "atoms" is derived based on the model of "pure" matter. This model represents the equilibrium Coulomb system of interacting electrons and nuclei of the same type, using the adiabatic approximation for nuclei, the self-consistent Hartree-Fock approximation for the electronic subsystem, the "one-center" approximation to describe localized electronic states, and the perturbation theory with respect to the fluctuating field. It is shown that the found potential is completely defined by the inhomogeneous density and inhomogeneous density matrix of electronic states in the isolated "atom"