Ground-State Energy and Excitation Spectrum of a System of Interacting Bosons

BEC from a time-dependent variational point of view

“…We then obtain the implicit solutions: with q = ξ + n. This is obtained by setting α = 2φ + π which is compatible with the Hugenholtz-Pines theorem [21] expressed in our context by the identity |m0| = ξ + n +ñ0.…”

Thermodynamics of Ultracold Fermi Gases

“…, (5.15) where the non-analytical log term is given by the low-k divergence and is universal. The coe cient B is not universal and depends on the precise shape of the interaction potential [212]. In [213] an explicit expression for B is proposed, based on the study of a gas of hard spheres: 16) involving the following parameters:…”

Nonequilibrium Relaxation of Bose–Einstein Condensates: Real-Time Equations of Motion and Ward Identities

“…Assuming that the condensate φ 0 is real, which can always be made by a gauge transformation (2.14), the above expression is recognized as the HugenholtzPines relation [22].…”

“…For a homogeneous Bose gas in the condensed phase a classification scheme for the different types of theoretical approximations to study the excitations has been put forth in a seminal article by Hohenberg and Martin [21] and more recently discussed in detail by Griffin [6,14,8]. A very important ingredient for a consistent description of the dynamics of quasiparticle excitations is the Hugenholtz-Pines theorem [22], which is a consequence of the underlying gauge invariance [21] and similar to the Goldstone theorem in that it guarantees gapless single (quasi)particle excitations if a continuous symmetry is broken with short range forces [23]. Since the Hugenholtz-Pines theorem is a consequence of the original gauge invariance and the Ward identities that stem from it, it is important to guarantee that any approximation scheme to study the dynamics of low energy excitations respects this theorem [14].…”