Studying creation of bulk elementary excitation by heaters in superfluid helium-II at low temperatures

In this paper, the obtained experimental results concerning creation of bulk elementary excitations （BEEs） in isotopically pure liquid ^4He at low temperatures -60 mK are discussed. Positive rotons＇ （R^＋-rotons） creation by a pulsed heater was studied. Signals were recorded for the following quantum processes： quantum evaporation of ^4He-atoms from the free liquid-helium surface by the BEEs of the liquid helium-Ⅱ, and BEEs reflection from the free surface back into the bulk liquid. Typical signals are shown, and ratios of signal amplitudes are evaluated. For long heater pulses from 5 to 10 μs, appearance of the second atomic cloud consisting of evaporated ^4He-atoms was observed in addition to the first atomic cloud. It is thought that the first atomic cloud of the evaporated helium atoms consists of very fast ^4He-atoms with energies ～35 K evaporated by positive rotons with the special energies ～17 K （～2ER～2×8.6 K with ER representing the roton minimum energy） corresponding to the third non-dispersive Zakharenko wave. The second cloud of slower ^4He-atoms was created by surface elementary excitations （SEEs or ripplons） possessing the special energies ～7.15 K representing the binding energy. It was assumed that such SEEs can be created by phonons incoming to the liquid surface with special energies ～6.2 K corresponding to the first non-dispersive Zakharenko wave which can interact at the liquid surface with the same phonons already reflected from the surface for long heater pulses. Also, some pulsed-heater characteristics were studied in order to better understand the features of such heaters in low temperature experiments.

Excitation spectrum and structure factor of a two-component Bose-Einstein condensate in different hyperfine states

The elementary excitation spectrum of a two-component Bose-Einstein condensate in different hyperfine states is obtained by Green＇s function method. It is found to have two branches. In the long wave-length limit, the two branches of the excitation spectrum are reduced to one phonon excitation and one single-particle excitation. The single-particle one has an energy gap. When the energy gap exists, we study the Landau critical velocity and the depletion of the condensate. With the obtained Green＇s functions, we calculate the structure factor of a two-component condensate. It is found that the static structure factor comprises only the branch of the phonon excitation and the single-particle excitation makes no contribution to the structure factor.

On the ground state energy of the inhomogeneous Bose gas

Within the self-consistent Hartree^Fock approximation, an explicit in this approximation expression for the ground state energy of inhomogeneous Bose gas is derived as a functional of the inhomogeneous density of the Bose-Einstein condensate. The results obtained are based on existence of the off-diagonal long-range order in the single-particle density matrix for systems with a Bose-Einstein condensate. This makes it possible to avoid the use of anomalous averages. The explicit form of the kinetic energy, which differs from one in the Gross-Pitaevski approach, is found. The obtained form of kinetic energy is valid beyond the Hartree--Fock approximation and can be applied for arbitrary strong interparticle interaction.