Keldysh’s theory of a rarefied superfluid electron-hole gas is extended to the case of possible pair polarization. It is established that the complex order parameter Φ(r1,r2), which is the wave function of a pair, satisfies a nonlinear, nonlocal, integrodifferential equation. The equation obtained is solved for the order parameter varying slowly over a distance of the order of the pair size. The dipole-moment density of the system is found from the known function Φ(r1,r2), and it is shown that the inhomogeneity of the system engenders a dipole moment proportional and oriented parallel to the gradient of the particle density. It is determined that an additional dipole moment associated with pair polarization due to the Lorentz force appears in a magnetic field.
The Keldysh's theory of superfluidity of rarefied electron-hole gas is generalized to a case of possible pair polarizability. It was shown that inhomogeneity of the system leads to dipole moment which is proportional to the density gradient. The dipole moment appears also near boundaries of the system. It was determined that quantized vortices in a magnetic field carry a real electric charge. In He II at H=10 T and helium rotation velocity $10^2$ s$^{-1}$ the charge density is about $10^4e$ cm$^{-3}$, where $e$ is the electron charge.Comment: 5 pages V. 2: replaced incorrect g valu
The issue of adequate describing a gas of complex particles, composed of an even number of fermions, as point bosons is studied in alkali metals. In the low-density approximation we obtain the equation for the complex order parameter Φ(r1, r2) representing the wave function of atoms with taking into account the internal motion of the valence electrons. For superfluid systems formed by particles with internal degrees of freedom, this equation replaces the Gross-Pitaevskii equation. It is shown that, in general, exchange effects should be considered in the same approximation as effects of the direct interaction of atoms with each other. In particular, in the case of only the Coulomb interaction the neglect of exchange effects leads to qualitatively incorrect results. The problem of spontaneous polarization in superfluid systems is studied. The expression for the electric polarization of the inhomogeneous superfluid system is obtained.
The electric polarization appearing in superfluid systems as a result of their inhomogeneity is studied. The problem is studied using the rarefied electron-hole gas model which the authors studied previously. A microscopic calculation is performed of the polarization of quantum vortices in the absence and presence of a magnetic field. It is established that in the presence of a magnetic field vortices acquire additional polarization, which results in the appearance of a quantized charge in a vortex core. It is shown that the van-der-Waals interaction of a superfluid system with a solid surface gives rise to polarization near the surface. A relation is established between the results obtained and the prediction of possible polarization of the medium in nonuniform motion.
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