Thermodynamics of the Fermi gas in a nanotube

For the ideal Fermi gas that fills the space inside a cylindrical tube, there are calculated the thermodynamic characteristics in general form for arbitrary temperatures, namely: the thermodynamic potential, energy, entropy, equations of state, heat capacities and compressibilities. All these quantities are expressed through the introduced standard functions and their derivatives. The radius of the tube is considered as an additional thermodynamic variable. It is shown that at low temperatures in the quasi-one-dimensional case the temperature dependencies of the entropy and heat capacities remain linear. The dependencies of the entropy and heat capacities on the chemical potential have sharp maximums at the points where the filling of a new discrete level begins. The character of dependencies of thermodynamic quantities on the tube radius proves to be qualitatively different in the cases of fixed linear and fixed total density. At the fixed linear density these dependencies are monotonous and at the fixed total density they have an oscillating character. Key words: Fermi particle, nanotube, thermodynamic functions, low-dimensional systems, equation of state, heat capacity, compressibilityComment: 12 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1608.0720

The equation of state and the quasiparticle mass in the degenerate Fermi system with an effective interaction

General formulas are derived for the quasiparticle effective mass and the equation of state of the Fermi system with account of the interparticle attraction at long distances and repulsion at short distances. Calculations are carried out of the equation of state and the effective mass of the Fermi system at zero temperature with the use of the modified Morse potential. It is shown that the pair repulsive forces promote a decrease of the effective mass, and the attractive forces promote its increase. With a certain choice of the parameters of the potential the dependence of the pressure on the density has a nonmonotonic character, which enables to describe the coexistence of the liquid and gaseous phases. The influence of three-body interactions on the equation of state and the effective mass is considered. The calculation results are compared with experimental data concerning the quasiparticle effective mass in the liquid $^3$He. Key words: normal Fermi liquid, effective mass, quasiparticle, equation of state, interaction potentialComment: 10 pages, 3 figure

The self-consistent field model for Fermi systems with account of three-body interactions

On the basis of a microscopic model of self-consistent field, the thermodynamics of the many-particle Fermi system at finite temperatures with account of three-body interactions is built and the quasiparticle equations of motion are obtained. It is shown that the delta-like three-body interaction gives no contribution into the self-consistent field, and the description of three-body forces requires their nonlocality to be taken into account. The spatially uniform system is considered in detail, and on the basis of the developed microscopic approach general formulas are derived for the fermion's effective mass and the system's equation of state with account of contribution from three-body forces. The effective mass and pressure are numerically calculated for the potential of "semi-transparent sphere" type at zero temperature. Expansions of the effective mass and pressure in powers of density are obtained. It is shown that, with account of only pair forces, the interaction of repulsive character reduces the quasiparticle effective mass relative to the mass of a free particle, and the attractive interaction raises the effective mass. The question of thermodynamic stability of the Fermi system is considered and the three-body repulsive interaction is shown to extend the region of stability of the system with the interparticle pair attraction. The quasiparticle energy spectrum is calculated with account of three-body forces.Comment: 21 pages, 5 figure

Роль гітлерівського та сталінського режимів у посиленні конфронтації між українським і польським населенням на західноукраїнських землях

На основі документальних та історіографічних джерел досліджуються підступні дії та наміри нацистської Німеччини та тоталітарного радянського режиму у загостренні міжетнічного польсько-українського протистояння в роки Другої світової війни. Показана синхронність дій як гітлерівського так і сталінського режимів на початковому етапі війни, коли створювалися видимість «підтримки» українців у Генеральному губернаторстві та ілюзія встановлення «української влади» на західноукраїнських землях. Розкриті форми колонізації окупованих земель німецькими загарбниками: виселення корінного населення, провокування відплатних акцій, утворення етнічних поліцейських частин. Висвітлена роль керівництва радянського партизанського руху у використанні польського населення для розпалювання протидії українському націоналістичному підпіллю. Показана відступна діяльність спецгруп НКВС, які одночасно чинили напади на українські і польські села, прикриваючись українськими і польськими патріотичними гаслами. Документальні джерела засвідчують, що у кінцевому результаті польсько-українське збройне протистояння обезкровлювало і послаблювало їх національні сили у боротьбі проти справжніх ворогів їх державної незалежності

Degenerate Odd Poisson Bracket on Grassmann Variables

A linear degenerate odd Poisson bracket (antibracket) realized solely on Grassmann variables is presented. It is revealed that this bracket has at once three nilpotent $\Delta$-like differential operators of the first, the second and the third orders with respect to the Grassmann derivatives. It is shown that these $\Delta$-like operators together with the Grassmann-odd nilpotent Casimir function of this bracket form a finite-dimensional Lie superalgebra.Comment: 5 pages, LATEX. Corrections of misprints. The relation (23) is adde

Phonon and optical-roton branches of excitations of the Bose system

For a system of a large number of Bose particles, a chain of coupled equations for the averages of field operators is obtained. In the approximation where only the averages of one field operator and the averages of products of two operators at zero temperature are taken into account, there is derived a closed system of dynamic equations. Taking into account the finite range of the interaction potential between particles, the spectrum of elementary excitations of a many-particle Bose system is calculated, and it is shown that it has two branches: a sound branch and an optical branch with an energy gap at zero momentum. At high density, both branches are nonmonotonic and have the roton-like minima. The dispersion of the phonon part of the spectrum is considered. The performed calculations and analysis of experiments on neutron scattering allow to make a statement about the complex structure of the Landau dispersion curve in the superfluid He-4.Comment: 18 pages, 6 figure