Identities and Many-Body Approaches in Bose-Einstein Condensates

Abstract

This paper discusses exact relations in Bose-Einstein condensates (BECs), starting from basic properties of an ideal Bose gas. In particular, focused on are the Hugenholtz-Pines relation, Nepomnyashchii-Nepomnyashchii identity, and identities for the density response function. After introducing these exact relations, a few approaches of many-body approximations are discussed, which satisfy the exact relations in BECs. This paper will serve as a bridge between theories on exact relations and those on approximations in BECs.

Bose-Einstein condensation phenomenology in systems with repulsive interactions

“…The purely repulsive interactions correspond to dU/dn > 0. The MF model with U (n) = an, a > 0, (19) was applied to describe the BEC of interacting bosons in Ref. [43].…”

“…In the MF model [Eqs. (16)- (19)] the BEC line corresponds to the effective chemical potential being equal to the particle's mass, μ * = m. Therefore, as follows from Eq. (17) the density, n, and temperature, T c , at the BEC line are connected by the same equation as for the Id-BG case:…”

“…The theory of the BEC phenomenon for interacting particles has been extensively discussed [15][16][17][18][19]. In particular, modifications of the BEC onset line (further referred to as the BEC line) due to the small repulsive interactions between particles were predicted [20][21][22][23][24][25][26].…”

Phase diagram of interacting pion matter and isospin charge fluctuations

“…[7][8][9][10][11][12][13][14][15]). A theoretical description of the BEC appears to be rather sensitive to delicate details of particle interactions [16][17][18][19][20][21][22][23][24][25].…”

Strong connection between single-particle and density excitations in Bose-Einstein condensates

“…The formulation in these sections, where the earlier result by Gavoret and Nozières [9] and the subsequent result by Nepomnyashchii and Nepomnyashchii [35,36] are revisited, is developed in the matrix formalism. This formalism can easily address structures of diagrams and infrared divergences in BECs [34,[37][38][39], which has been successfully applied to reproduce the Nepomnyashchii-Nepomnyashchii identity [38]. Section V reviews the earlier experimental and theoretical studies focused on the sound mode in the superfluid helium as well as ultracold atomic BECs, where variant sound modes in the superfluid, such as the second sound, are important but beyond the scope of the present paper.…”