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Low Temperature Physics

Coulomb interaction potential and Bose-Einstein condensate

Viktor Borisovich Bobrov, Anatolij G. Zagorodny, S. A. Trigger

Published Nov 1, 2015• 13 citations
Publisher

Abstract

Based on the results of statistical quantum electrodynamics, it is shown that the Coulomb interaction potential of charged particles has no Fourier components at a zero wave vector. This result provides for the possibility of using the grand canonical ensemble to describe the Coulomb system, with independent descriptions of different varieties of charged particles. Based on this, we established that there could be an energy gap in the single-particle excitation spectrum at low pulses, given the presence of Bose-Einstein condensate in the Coulomb system, which does not contradict the existence of collective excitations, characterized by the phonon-roton spectrum.

DOI
10.1063/1.4936669

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Based on the results of statistical quantum electrodynamics, it is shown that the Coulomb interaction potential of charged particles has no Fourier components at a zero wave vector. This result provides for the possibility of using the grand canonical ensemble to describe the Coulomb system, with independent descriptions of different varieties of charged particles. Based on this, we established that there could be an energy gap in the single-particle excitation spectrum at low pulses, given the presence of Bose-Einstein condensate in the Coulomb system, which does not contradict the existence of collective excitations, characterized by the phonon-roton spectrum.
An expression for the short-range effective interaction potential of “quasinuclei” is derived based on the “pure” Coulomb interaction model. This model represents the equilibrium Coulomb system (CS) of interacting electrons and identical nuclei using the adiabatic approximation for nuclei and an arbitrarily strong (in general) interaction for the electronic subsystem (degenerate or nondegenerate). Based on general properties of the Coulomb interaction, it is shown that the Fourier component of the effective pair potential between “quasinuclei” is discontinuous at the wave vector q = 0 in the case of the weak interaction between electronic and nuclear subsystems. This discontinuity is important for Bose-condensed systems such as Hell and rarefied alkali-metal gases at temperatures lower than that of the Bose condensation transition when a macroscopic number of quasiparticles with momentum q = 0 exist. It is shown that there can be a spectral gap for single-particle excitations, which disappears in the normal state.
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's function exactly coincides with the Bogolybov's phonon-roton spectrum of excitations. At the same time, a gap exists in the one-particle excitation spectrum . This gap is related to the density of particles in the "condensate".
The aim of this work is to investigate how energy depends on the two-body interaction potential in Bose-Einstein condensation (BEC) phenomena. An equation of state is obtained which is valid both for low and high energy BEC, through the application of a revised form of quantum statistics. An extension of the singularity conditions describing the state of BEC is given, in order to consider interactions between particles due to a central interatomic potential. From the singularity conditions of the corresponding system of hard-sphere bosons and the equation for the energy of the system in its ground state, the equation of state connecting temperature, density and energy in BEC is deduced, with upper and lower limits for the energy depending on the form of the central interaction potential. It is shown that high energy mode is allowed in the case of Coulomb type interaction only, low energy mode in the case of non-Coulomb type interaction. Numerical results are then derived for low energy BEC, occurring in neutral matter, with application to He-4 and alkali-metal atoms, and in the case of high energy BEC occurring in systems of charged bosons, with application to atomic nuclei.
Abstract In this article a system containing two species of identical bosons interacting via a harmonic oscillator potential is considered. It is assumed that the number of bosons of each species is the same and that bosons belonging to the same species repel each other while those belonging to different species attract. The Hamiltonian is diagonalized and the energy spectrum of the system is written down. The behaviour of the system in the thermodynamic limit is studied within the framework of the grand canonical ensemble, and thermodynamic parameters, such as the internal energy, entropy and specific heat capacity are calculated. It is shown that the system exhibits a single species Bose–Einstein condensation when the coupling strengths are equal and a dual species condensation when they are different.
The Bogoliubov treatment of a weakly interacting Bose gas is extended by allowing macroscopic occupation of many single-particle quantum states. This generalization of having more than a single condensed mode gives rise to a nonuniform condensate and is being considered as a possible mechanism for the description of a dense strongly interacting Bose gas at low temperatures. The model with a repulsive $\ensuremath{\delta}$-function interparticle potential gives an energy spectrum of elementary excitations or quasiparticles with both phonon and roton features. The values obtained for the roton minimum energy $\ensuremath{\Delta}$ and the speed of (first) sound agree reasonably well with inelastic-neutron-scattering data.