Microscopic theory of the energy spectrum of liquid He II

First sound velocity in liquid ^{4}He

“…The other way to the same result goes through formula [24,26]: 5) where the valueã 2 (q) has such a look:…”

“…Particularly in papers [24,26], correlation was found between the first sound velocity at absolute zero temperature and the Fourier coefficient of pair interparticle interaction energy in the "one sum over the wave vector" approximation. This result was obtained in two different ways.…”

“…Theoretical study of the sound velocity was also carried out by the collective variables representative method, but only in the limit of low temperatures [23][24][25][26][27]. Particularly in papers [24,26], correlation was found between the first sound velocity at absolute zero temperature and the Fourier coefficient of pair interparticle interaction energy in the "one sum over the wave vector" approximation.…”

Theory of structure and thermodynamic function of liquid 4He (Review Article)

“…Notwithstanding the fact that it is obvious, this formula makes it possible to fully restore the density matrix (8). Here most significant heuristically is an arbitrary choice of the function () x on condition that it is nonorthogonal to the eigenfunctions of the Ĥ operator and the existence of integral (6).…”

“…The wavefunction of the first excited state and the equation for the excitation spectrum were built in Ref. 8. It was shown in the first order of perturbation theory that correction to the sound velocity and damping of the spectrum coincide with the results of field-theoretical approach [9].…”