arXiv subjects
Publications and source records attributed to Yu. M. Poluektov.
A relativistic equation for a neutral complex field as a probability amplitude is proposed. The continuity equation for the probability density is obtained. It is shown that there are two types of excitations of this field, which describe particles with positive energy and different dispersion laws. Based on the Lagrangian formalism, conservation laws are obtained. The transition to secondary quantization is considered.
A method for describing charged relativistic Fermi fields is proposed, in which particles of opposite charges are treated equally and states with negative energy are excluded. The concept of charge quantum number is introduced. Fields of particles and antiparticles with different charge quantum numbers are associated with wave functions for which the Born interpretation as probability amplitudes is valid.
A statistical approach to the description of the thermodynamic properties of the Fermi particle system occupying a half-space over a plane of finite size in a uniform external field is proposed. The number of particles per unit area is assumed to be arbitrary, in particular, small. General formulas are obtained for entropy, energy, thermodynamic potential, heat capacities under various conditions and the distribution of the particle number density over the surface. In the continuum limit of a large surface area, the temperature dependences of heat capacities and density distribution are calculated. The cases of gravitational and electric fields are considered.
Thermodynamic functions of the ideal Fermi gas at arbitrary temperatures are calculated using the standard Fermi-Stoner functions. The properties of the Fermi-Stoner functions are analyzed. The limiting cases of low-temperature and classical limits with taking into account quantum corrections and the special case of zero chemical potential are considered.
In the weakly non-ideal gas model [1], the Bose-Einstein condensation at constant pressure is considered. The temperature of transition to the state with condensate is found. Temperature dependences of the total density and condensate density, the energy, entropy and heat capacities are calculated.
On the example of a quantum oscillator the connection of the dynamical coherent state with the phase symmetry breaking and the existence of the nondissipative motion is considered. In multiparticle systems of interacting particles similar states manifest themselves as super uidity and superconductivity.
For the Fermi gas filling the space inside a cubic cavity of a fixed volume, at arbitrary temperatures and number of particles, the thermodynamic characteristics are calculated, namely: entropy, thermodynamic potential, energy, pressure, heat capacities and thermodynamic coefficients. The discrete structure of energy levels is taken into account and size effects at low temperatures are studied. The transition to the continual limit is considered.
Equations are obtained for the quantum distribution functions over discrete states in systems of non-interacting fermions and bosons with an arbitrary, including small, number of particles. The case of systems with two levels is considered in detail. The temperature dependences of entropy, heat capacities and pressure in two-level Fermi and Bose systems are calculated for various multiplicities of degeneracy of levels.
Expressions for the entropy and equations for the quantum distribution functions in systems of non-interacting fermions and bosons with an arbitrary, including small, number of particles are obtained in the paper
The relativistic quantum equation is proposed for the complex wave function, which has the meaning of a probability amplitude. The Lagrangian formulation of the proposed theory is developed. The problem of spreading of a wave packet in an unlimited space is solved. The relativistic correction to the energy levels of a harmonic oscillator is found, leading to a violation of their equidistance.
A suggested amendment to the temperature dependencies in the thermodynamic potential of the Ginzburg-Sobyanin theory of superfluidity, which makes it possible to obtain critical exponents that are consistent with the general relations of the fluctuation theory of phase transitions, as well as with modern experimental and calculated data.
Classical and quantum complex nonlinear scalar fields are considered. A new approach to the quantization of nonlinear fields and the construction of a perturbation theory with allowance for spontaneous symmetry breaking is proposed, based on the use of the relativistic model of a self-consistent field as the main approximation. The concept of a particle is analyzed within the frame-work of the theory of nonlinear quantum fields. When constructing single-particle states, the contribution of vacuum fluctuations is systematically taken into account. Within the framework of the developed approach, the problem of the existence of massless scalar particles is discussed. It is shown that successive consideration of the vacuum averages of not only one field operator, but also the products of two field operators, leads to the appearance of masses for scalar particles. Various states in which the field can exist for given parameters entering into the Lagrangian are considered, and the vacuum energy densities in these states are calculated. It is shown that, depending on the values of the parameters entering into the Lagrangian, the vacuum energy density can be either positive or negative, which is important for modern cosmology.
In the framework of the theoretical model of the phase transition of binary solutions into spatially inhomogeneous states proposed earlier by the autors [1], which takes into account nonlinear effects, the role of the cubic in concentration term in the expansion of free energy was studied. It is shown that taking into account the cubic term contributions to the stabilization of a homogeneous state. The existence of two inhomogeneous phases in an isotropic medium, considered in [1], proves to be possible only at half the concentration of the solution. The contribution of inhomogeneity effects to thermodynamic quantities is calculated. Phase transitions from a homogeneous state and between inhomogeneous phases are second-order phase transitions.
The phase transition to the state of a phonon gas with pairwise correlations of interacting phonons with opposite momenta is studies. A method for describing such phonon systems within the framework of the self-consistent field model is developed and their thermodynamic characteristics are calculated. It is shown that a phonon gas with pair correlations can exist in a state of unstable thermodynamic equilibrium. The possibility of experimental observation of a solid in such a phase is discussed.
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.
The thermodynamics of phase transitions of binary solutions into spatially inhomogeneous one-dimensional states is studied theoretically with taking into account nonlinear effects. It is shown that below the spinodal decomposition temperature there first occurs a phase stratification, and at a lower temperature, after reaching the maximum possible stratification, there occurs a second-order transition into the phase with concentration waves. The contribution of inhomogeneity to the entropy and heat capacity of phases is calculated and the phase diagram in the coordinates temperature and average concentration is constructed.
A semi-phenomenological model of a many-particle system of 4He atoms is proposed, in which a helium atom is considered as a complex consisting of a nucleus and a bound pair of electrons in the singlet state. At zero temperature, there are two Bose-Einstein condensates of particles with opposite charges, namely, a condensate of positively charged nuclei and a condensate of negatively charged electron pairs. It is shown that in such a system there exist two excitation branches: sound and optical. On the basis of this model an interpretation of experiments on the study of the eltctrical activity of superfluid heliun is proposed. The frequency at which the resonant absorption of a microwave radiation is observed is interpreted as a gap in the optical branch. It is shown that the distribution of the electric potential in a standing wave in a resonator is similar to that observed experimentally.
A quantum description of the surface waves in an isotropic elastic body without the use of the semiclassical quantization is proposed. The problem about the surface waves is formulated in the Lagrangian and Hamiltonian representations. Within the framework of the generalized Debye model, the contribution of the surface phonons (rayleighons) to thermodynamic functions is calculated. It is emphasized that the role of the surface phonons can be significant and even decisive in low-dimensional systems, granular and porous media, and that their contribution to the total heat capacity increases with decreasing temperature.