One-particle density matrix of liquid 4He

Abstract

Using the expression for the total density matrix for a system of N interacting Bose particles found in our previous papers, we calculate the one-particle density matrix in the coordinate representation. At low temperatures, the leading approximation of this matrix reproduces the results of the Bogoliubov theory. In the classical limit, the proposed theory reproduces the results of the theory of the classical liquid in the approximation of chaotic phases. From the one-particle density matrix, we find the particle momentum distribution function and the mean kinetic energy of the Bose liquid and investigate the phenomenon of Bose-Einstein condensation.With gratitude and warmness, the author recollects the numerous meetings and conversations with Dmitrii Nikolaevich Zubarev, his advice and constant support, and dedicates this paper to the memory of the scientist who did so much to develop the foundations of statistical mechanics, a person of high culture, fine soul, and exceptional intellectuality.

Effective Mass of 4He Atom in Superfluid and Normal Phases

“…where the quantity m(p) is regarded as the total effective mass of a particle, which depends on the absolute value of wave vector p. This form for the spectrum εp was proposed in work [27] in order to exclude infra-red divergences. It will be recalled that the effective mass m is formed by many-particle correlations, starting from four-particle ones, and, generally speaking, it depends on the momentum p. It is clear that we are interested in the behavior of m(p) as p → 0.…”

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

“…First of all we will discuss the possible way of the density matrix calculation taking into account the two-particle interatomic correlations. The presence of off-diagonal long-range order of the one-particle density matrix, which can be calculated using the density matrix [24] is the indication of the phase transition in this approach. The order parameter of the theory is the value 1/2 0 ( / ) ,…”