Integral representations of the classical KMS-states for quasi-free evolutions

We investigate the validity of the Bogoliubov c-number approximation in the case of interacting Bose-gas in a \textit{homogeneous random} media. To take into account the possible occurence of type III generalized Bose-Einstein condensation (i.e. the occurrence of condensation in an infinitesimal band of low kinetic energy modes without macroscopic occupation of any of them) we generalize the c-number substitution procedure to this band of modes with low momentum. We show that, as in the case of the one-mode condensation for translation-invariant interacting systems, this procedure has no effect on the exact value of the pressure in the thermodynamic limit, assuming that the c-numbers are chosen according to a suitable variational principle. We then discuss the relation between these c-numbers and the (total) density of the condensate

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“…in some weak sense, see e.g. [3]. These ideas were exploited to construct a various truncations of the full interacting boson Hamiltonian.…”

Section: Motivationmentioning

confidence: 99%

Exactness of the Bogoliubov approximation in random external potentials

Jaeck

Zagrebnov²

2010

Journal of Mathematical Physics

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“…where a(f ) = f (x)a(x)dx for f ∈ C ∞ 0 (R ν ), f is the Fourier transform of f and ρ 0 is the condensate density. It is proved in [20] that (13) implies, amongst other things, the breaking of the gauge symmetry.…”

Section: The Model and Equilibrium Statesmentioning

confidence: 99%

Goldstone Boson Normal Coordinates

Michoel¹,

Verbeure²

2001

Communications in Mathematical Physics

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“…In the seventies, G. Gallavotti and E. Verboven, suggested a classical analogue to the quantum KMS condition suitable for classical mechanical systems and they analysed its relationship with the Dobrushin-Lanford-Ruelle (DLR) equation, see [33] and also [1]. The work of Gallavotti and Verboven generated interest in the study of KMS states for infinite classical systems (see for instance [26,54] and the references therein). To the best of our knowledge, only few results are concerned with nonlinear PDEs, namely [9,24,53].…”

Section: Introductionmentioning

confidence: 99%