Coulomb interaction potential and Bose-Einstein condensate

Abstract

Based on the results of statistical quantum electrodynamics, it is shown that the Coulomb interaction potential of charged particles has no Fourier components at a zero wave vector. This result provides for the possibility of using the grand canonical ensemble to describe the Coulomb system, with independent descriptions of different varieties of charged particles. Based on this, we established that there could be an energy gap in the single-particle excitation spectrum at low pulses, given the presence of Bose-Einstein condensate in the Coulomb system, which does not contradict the existence of collective excitations, characterized by the phonon-roton spectrum.

Конденсат Бозе - Эйнштейна И Особенности Частотной Дисперсии Диэлектрической Проницаемости В Неупорядоченной Кулоновской Системе

“…Следует отметить, что для интерпретации экспериментально наблюдаемого резонансного поглощения в сверхтекучем He-II к настоящему времени предложено множество различных моделей (подробная библиография по этому вопросу представлена в [38], [39]). Предлагаемый эксперимент по исследованию отражения электромагнитных волн от поверхности сверхтекучего He-II позволит однозначно решить вопрос о наличии одночастичного КБЭ в сверхтекучем He-II.…”

From the Coulomb to Effective Interaction: Application to Bose—Einstein Condensation

“…We notice, that in this case condition (1) is no way affects the form of the Coulomb interaction potential v a,b (r) in the r-space. However, as it is shown in [16] (see also [18], [19]) equality (1) cannot be rigorously justified in the framework of classical theory and requires consideration on the basis of quantum electrodynamics. Thus, when constructing the statistical theory for the quantum non-relativistic CS, instead of the integral Fourier transform (2) for the Coulomb potential, the Fourier series…”

“…Following to [18], [19], to solve the problem of the value of v a,b (q = 0) = 0, it is necessary to turn to the results of the quantum field theory (e.g., [23]) according to which charged particles interact with each other through the quantized electromagnetic field. Within quantum statistical electrodynamics [24], we can speak of the correspondence between the Green function for the quantized electromagnetic field D µ,ν (k) (µ, ν = 0, 1, 2, 3; k = (ω/c, q)) and the interaction potentials between charged particles.…”

“…where Π e (q) is the polarization function for electron liquid with arbitrary strong interaction, v e,n = −4πZ n e 2 /q 2 and v n,n = 4πZ 2 n e 2 /q 2 . According to relation (1) [16] (see also [18], [19] and [5]) the value of v ef f n,n (q=0) = 0, since Π e (q=0) is finite. At the same time for q → 0 from (6) we arrive at the value v ef f n,…”

On the ground state energy of the inhomogeneous Bose gas

“…Such approach allows the self-consistent consideration of BEC by transferring to the thermodynamic limit [17] (see [18] for more details). On this basis we establish in the present paper two new results: a) the explicit expression for kinetic part of the ground state energy of Bose system with BEC in an external field, which is valid for arbitrary strong interaction between particles, b) the ground state energy of the system under consideration in the Hartree-Fock approximation, which differs from one in the theory, based on anomalous averages.…”