On the ground state energy of the inhomogeneous Bose gas

Within the self-consistent Hartree-Fock approximation, an explicit expression for the ground state energy of inhomogeneous Bose gas is derived as a functional of the inhomogeneous density of the Bose-Einstein condensate. The results obtained are based on existence of the off-diagonal long-range order in the single-particle density matrix for systems with a Bose-Einstein condensate. This makes it possible to avoid the use of anomalous averages. The explicit form of the kinetic energy, which differs from one in the Gross-Pitaevski approach, is found. This form is valid beyond the Hartree-Fock approximation and can be applied for arbitrary strong interparticle interaction.Comment: 4 pages, 0 figure

Theory of degenerate Bose gas without anomalous averages

Theory of a weakly non-ideal Bose gas in the canonical ensemble is developed without assumption of the C-number representation of the creation and annihilation operators with zero momentum. It is shown that the pole of the "density-density" Green function exactly coincides with the Bogolybov's phonon-roton spectrum of excitations. At the same time in the one-particle excitation spectrum a gap exists. The value of this gap is connected with the density of particles in the "condensate".Comment: 7 pages, no figure

Collective excitations and the gap in spectrum of the degenerated Bose gas

Model of the degenerated weakly non-ideal Bose gas is 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 are calculated on basis of the suggestion about C-number representation of the operator of particle density in the Bose condensate. It is shown, that the pole in the "density-density" Green function determines the Bogolyubov's spectrum of the collective excitations, which have the phonon-roton form. At the same time the spectrum of the one-particle excitations possesses a gap, whose value is connected with the density of particles in the Bose condensate.Comment: 7 pages, no figure

Density functional theory and free energy of inhomogeneous electron gas

It is shown that in adiabatic approximation for nuclei the many-component Coulomb system cannot be described on the basis of the grand canonical ensemble. Using the variational Bogolyubov's procedure for the free energy, the Hohenberg-Kohn theorem is proved in the canonical ensemble for inhomogeneous electron gas at finite temperature. The principal difference between consideration in the framework of quantum statistics in the canonical ensemble and quantum-mechanical consideration of a finite number of particles in infinite volume is established. The problem of universality of the density functional for describing the inhomogeneous electron density in a disordered nuclei field is considered.Comment: 13 pages, no figure

Frequency depending permittivity of the Coulomb system with Bose-Einstein condensate

The second-order singularity is found in the low-frequency region of the permittivity of a homogeneous and isotropic system of charged particles consisting of electrons and boson nuclei. This singularity is caused by the existence of a Bose-Einstein condensate for nuclei. The result obtained leads to the existence of the "nuclei superconductivity", which can be experimentally verified in superfluid He II. The results of the proposed an experiment can be considered as a direct proof of the existence of a Bose-Einstein condensate in superfluid He II.Comment: 13 pages, 0 figure

Universality of rotons in liquids, generalized superfluidity criterion and helons in helium II

An analysis of experimental data shows that, in addition to phonon--roton excitations in superfluid helium, there necessarily exist at least one branch of elementary excitations whose energy spectrum strongly depends on temperature. On this basis, the Landau superfluidity criterion is generalized for several branches of elementary excitations, taking into account that the critical velocity should vanish during the phase transition of liquid helium from the superfluid state to the normal state. We suppose that a new spectrum of excitations with a gap, depending on interparticle interaction, corresponds to the transition of helium to superfluid state. This gap exists only in superfluid state and disappears at the transition temperature to normal state. The phonon-roton branch of excitations has no crucial influence on superfluidity. Rotons, as well as phonons, are not the specific excitations for the superfluid helium, but exist as universal excitations in liquid state, and form the continuous branch of excitations in different liquids. This point of view is confirmed experimentally and numerically.Comment: 13 pages, 4 figure

Ground state energy in the external field and the problem of density functional approximations

Based on the Schrodinger equation, exact expressions for the non-relativistic particle energy in the local external field and the external field potential are derived as inhomogeneous density functionals. On this basis, it is shown that, when considering more than two noninteracting electrons, the energy of such a system cannot be an inhomogeneous density functional. The result is extended for the system of interacting electrons. This means that the Hohenberg-Kohn lemma which assert that in the ground state to each inhomogeneous density corresponds only one potential of the external field cannot be a justification of the existence of the universal density functional in the general case. 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.Comment: 10 pages, 0 figure

Finite Size Atom in the Hartree-Fock Approximation: New Substance Quasiparticle

It is shown that, in the self-consistent quantum statistical Hartree-Fock approximation, the number of electronic states localized on one nucleus is finite. This result is obtained on the basis of the general electron-nuclear model of matter and provides convergence of the atomic statistical sum and finiteness of the "atom" size. In general approach the characteristic size of the "atom" is a function of density and temperature. However, it is shown, that in a wide range of thermodynamic parameters, for relatively low temperatures, characteristic orbits and electron energy eigenvalues are independent of density and temperature. In this case, the sizes of the orbits are of order of the Bohr radius which is a minimal characteristic size in the system for typical parameters of plasma with atomic states.Comment: 11 pages, 0 figure

Virial theorem and Gibbs thermodynamic potential for Coulomb systems

Using the grand canonical ensemble and the virial theorem, we show that the Gibbs thermodynamic potential of the non-relativistic system of charged particles is uniquely defined by single-particle Green functions of electrons and nuclei. This result is valid beyond the perturbation theory with respect to the interparticle interaction.Comment: 3 pages, no figure

From the density functional to the single-particle Green function

An analysis shows that the ground state of the inhomogeneous system of interacting electrons in the static external field, which satisfies the thermodynamic limit, can be consistently described only using the Green function theory based on the quantum field theory methods (perturbation theory diagram technique). In this case, the ground state energy and inhomogeneous electron density in such a system can be determined only after calculating the single-particle Green function.Comment: 9 pages, 0 figure