Hartree–Fock–Bogolubov Method in the Theory of Bose-Condensed Systems

Abstract

The Hohenberg-Martin dilemma of conserving versus gapless theories for systems with Bose-Einstein condensate is considered. This dilemma states that, generally, a theory characterizing a system with broken global gauge symmetry, which is necessary for Bose-Einstein condensation, is either conserving, but has a gap in its spectrum, or is gapless, but does not obey conservation laws. In other words, such a system either displays a gapless spectrum, which is necessary for condensate existence, but is not conserving, which implies that it corresponds to an unstable system, or it respects conservation laws, describing a stable system, but the spectrum acquires a gap, which means that the condensate cannot appear. An approach is described, resolving this dilemma, and it is shown to give good quantitative agreement with experimental data. Calculations are accomplished in the Hartree-Fock-Bogolubov approximation.

Superradiance by ferroelectrics in cavity resonators

“…The analysis of the evolution equations can be done by invoking a scale separation approach [48][49][50][51][52][53]55]. The pair spin correlators are decoupled by means of the stochastic mean-field approximation [48][49][50] giving…”

“…This equation has the same form as the Kirchhoff equation for a resonant electric circuit with a magnetic sample inside it. Therefore the consideration of the dipole dynamics in a ferroelectric can be done similarly to the study of spin dynamics in magnets [48][49][50][51][52][53].…”

“…of polarized nuclei, magnetic nanomolecules, magnetic nanoclusters, dipolar atoms and molecules, spinor atoms and molecules, and ferromagnets. Numerous citations can be found in review articles [48,49] and recent papers [50][51][52][53].…”

Magnetic equivalent of electric superradiance: radiative damping in yttrium-iron-garnet films

“…In both cases, a passive resonant electric circuit around the sample is necessary to produce the oscillating magnetic field which builds up the coherence of the relaxation of individual spins. 33,34 Recently, another magnetic alternative is proposed 35 where independent rare-earth magnetic moments are interacting with the spinwaves of the antiferromagnetically ordered iron spins in a magnetoelectric crystal. Here the expected superradiance of the rare-earth moments would appear as secondary-excited magnons of the iron system.…”

“…Since the magnetic resonance is excited coherently, the radiative broadening, caused by the re-emission of a secondary electromagnetic wave, is also originating from a coherent process, showing similarities to the superradiance broadening effect observed in the same frequency-range cyclotron resonance of a three-dimensional topological insulator 36 . Unlike other proposals of electron-spin superradiance [30][31][32][33][34] , our method does not require a surrounding passive electronic resonator circuit, since the amplification of the radiated mode is produced by the sample itself, as the substrate gadolinium gallium garnet (GGG) layer plays the role of the resonance cavity.…”