Number--conserving model for boson pairing

An independent pair ansatz is developed for the many body wavefunction of dilute Bose systems. The pair correlation is optimized by minimizing the expectation value of the full hamiltonian (rather than the truncated Bogoliubov one) providing a rigorous energy upper bound. In contrast with the Jastrow model, hypernetted chain theory provides closed-form exactly solvable equations for the optimized pair correlation. The model involves both condensate and coherent pairing with number conservation and kinetic energy sum rules satisfied exactly and the compressibility sum rule obeyed at low density. We compute, for bulk boson matter at a given density and zero temperature, (i) the two--body distribution function, (ii) the energy per particle, (iii) the sound velocity, (iv) the chemical potential, (v) the momentum distribution and its condensate fraction and (vi) the pairing function, which quantifies the ODLRO resulting from the structural properties of the two--particle density matrix. The connections with the low--density expansion and Bogoliubov theory are analyzed at different density values, including the density and scattering length regime of interest of trapped-atoms Bose--Einstein condensates. Comparison with the available Diffusion Monte Carlo results is also made.Comment: 21 pages, 12 figure

Binding Energy of Hydrogen-Like Impurities in Quantum Well Wires of InSb/GaAs in a Magnetic Field

The binding energy of a hydrogen-like impurity in a thin size-quantized wire of the InSb/GaAs semiconductors with Kane’s dispersion law in a magnetic fieldBparallel to the wire axis has been calculated as a function of the radius of the wire and magnitude ofB, using a variational approach. It is shown that when wire radius is less than the Bohr radius of the impurity, the nonparabolicity of dispersion law of charge carriers leads to a considerable increase of the binding energy in the magnetic field, as well as to a more rapid growth of binding energy with growth ofB