Comparative studies of many-body corrections to an interacting Bose condensate

Abstract

We compare many-body theories describing fluctuation corrections to the mean-field theory in a weakly interacting Bose-condensed gas. Using a generalized random-phase approximation, we include both density fluctuations and fluctuations in the particle-particle scattering channel in a consistent manner. We also separately examine effects of the fluctuations within the framework of the random-phase approximation. Effects of fluctuations in the particle-particle scattering channel are also separately examined by using the many-body T-matrix approximation. We assess these approximations with respect to the transition temperature, the order of phase transition, as well as the so-called Nepomnyashchii-Nepomnyashchii identity, which states the vanishing off-diagonal self-energy in the low-energy and low-momentum limit. Since the construction of a consistent theory for interacting bosons which satisfies various required conditions is a long standing problem in cold atom physics, our results would be useful for this important challenge.

23 pages, 9 figures

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• Green's function formalism for a condensed Bose gas consistent with infrared-divergent longitudinal susceptibility and Nepomnyashchii-Nepomnyashchii identity
• Identities and Many-Body Approaches in Bose-Einstein Condensates
• Strong connection between single-particle and density excitations in Bose-Einstein condensates
• Phase diagram of interacting pion matter and isospin charge fluctuations
• Large-$N$ properties of a non-ideal Bose gas
• Critical point influenced by Bose-Einstein condensation
• Condensation and superfluidity of $SU(N)$ Bose gas
• Hidden multiparticle excitation in weakly interacting Bose-Einstein Condensate
• Fock State Sampling Method -- Characteristic temperature of maximal fluctuations for interacting bosons in box potentials