The main focus of this work is on the predictions made by the dielectric formalism in regard to the relationship between single-particle and collective excitation spectra in a gas of pointlike charged bosons at finite temperature
T below the critical region of Bose-Einstein condensation. Illustrative numerical results at weak coupling
(rs=1) are presented within the random phase approximation. We show that within this approach the single-particle spectrum forms a continuum extending from the transverse to the longitudinal plasma mode frequency and leading to a double-peak structure as
T increases, whereas the density fluctuation spectrum consists of a single broad peak. We also discuss the momentum distribution and the superfluidity of the gas.
The generalized dielectric constant is calculated to the order next to the Bogoliubov approximation. This is done by using the analogy between the condensed boson system and a fictitious fermion system with spin degeneracy equal to the total number of particles (instead of two). From the zero of the dielectric constant, we have calculated the first-order correction to the Bogoliubov plasmon energy and the half linewidth of the plasmon states. The real part of the solution is examined from a graphical view point to show that up to the specified order of approximation there exists only one mode of elementary excitation. The screening of the system to a static impurity charge is shown to be exponential at a long distance. The response of the system to a static transverse vector potential shows a perfect Meissner effect at long- and short-wavelength limits. We have also examined the diagrammatic structure for the number of particles in condensate. We show that the series contains only terms of integer powers of
rs43. The entire treatment is fully number conserving.
The Bogoliubov-de Gennes equations and the Ginzburg-Landau-Abrikosov-Gor'kov-type theory are formulated for the charged Bose gas (CBG). The theory of the Bose-Einstein condensation of the CBG in a magnetic field is extended to ultralow temperatures and ultrahigh magnetic fields. A low-temperature dependence of the upper critical field
Hc2(T) is obtained both for the particle-impurity and particle-particle scattering. The normal-state collective plasmon mode in ultrahigh magnetic fields is studied.
The spectral properties of a mixture of bosons hybridized with fermion pairs are studied in the superconducting state. Such a model exhibits two limiting behaviors. One is reminiscent of a BCS system, provided that the total concentration n of particles is below a certain critical concentration
nc, in which case bosons exist only in thermally excited states. The other limit for n\ensuremath{\geqslant}
nc describes a situation largely controlled by the condensation of the bosons. The variation of the single-boson as well as collective excitations as a function of n and for the entire temperature regime from T=0 K to
Tc will be discussed, both with and without long-range Coulomb interaction between the charge carriers. The method for calculation applied here is based on the dielectric formalism and the use of Ward identities, currently used in the theory of the interacting Bose gas, which allows us to derive the density and current correlation functions consistent with local charge-current conservation laws. In the absence of a Coulomb interaction the behavior of the system is characterized by the existence of a sound-wave-like branch in the Bose single-particle and collective excitation spectrum. In the BCS regime the sound velocity is proportional to the Fermi velocity while in the Bose regime it is proportional to the strength of the boson-fermion hybridization and decreases with the superfluid density as we approach
Tc. In the presence of a long-range Coulomb interaction and in the Bose regime one observes, besides the usual optical plasmon mode at high frequency and corresponding to in-phase density oscillation of the two subsytems, an out-of-phase collective mode in the two particle continuum just above the gap. Moreover, upon approaching
Tc a relatively well-defined quasiparticle feature starts to emerge within the gap and is seen in both the Bose single-particle excitation and the density oscillation spectrum. In the BCS regime, due to the very small number of occupied bosonic states, the low-energy quasiparticle features are absent. \textcopyright{} 1996 The American Physical Society.
The ground state of a charged Bose gas is studied throughout a large range of densities in a self-consistent-field approximation formalism which includes the short-range correlations between bosons through a local-field correction. Numerical self-consistent calculations have been carried out in order to determine the static structure factor $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$. Hence, from $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ we have obtained the pair-correlation functions, the ground-state energy which essentially is the correlation energy, the pressure of the gas, and, from Feynman's relation, the energy spectrum of elementary excitations. The response of the system to a static impurity charge has also been investigated. In the high-density limit our calculations show the same results as those given by Bogoliubov's perturbation theory. In the intermediate-density region, corresponding to the strongly coupled system, our results are in very good agreement with recent calculations based on the hypernetted-chain integral equation as well as Monte Carlo computations.