Density matrices of a many-Boson system at low temperatures

One-particle density matrix of liquid 4He

“…which is the result we first found in [13]. We write the s-particle density p-matrix, which is nondiagonal in its first coordinate and diagonal with respect to all the other coordinates.…”

“…We first found expression (5.10) for the pair distribution function of the system of interacting Bose particles at T = 0 with effective potential (5.12) in [13]. At high temperatures in the semiclassical limit where β → 0, → 0, S 0 (q) → 1, and m * → m, by virtue of (2.9) and (4.3), we have λ q → βN ν(q)/V , and we then easily obtain the screened potential well-known in the theory of classical liquids,…”

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

“…Applying the method of coherent states it was also found in [28]. With the help of wave functions of the many-boson Bogoliubov-Zubarev system [5] it was calculated in [29,30]. Using our notations it looks as follows:…”

“…The problem of the partition function calculation is reduced to calculation of the functional integral (29). Let us pass to the calculation of average value of a product Here we formed average over the density matrix of ideal Bose gas and then used the representation (27) for the exponent term.…”

“…(29) to the so-called pair-particle correlation approximation 00 0 1 = exp ln 1 ( ) , 2 q I S q q then partition function (28) and two-particle structure factor () Sq (32) of Bose liquid in the pair-particle correlation approximation are…”