We consider spherically trapped Bose gases in three dimensions with contact interactions and investigate whether the Bose-Einstein condensate at zero temperature is stable against macroscopic fragmentation into a small number of mutually incoherent pieces. Our results are expressed in terms of a dimensionless interaction measure proportional to the Thomas-Fermi parameter. It is shown that while...

Sufficient conditions for a Lorentzian generalized quasi-Einstein manifold M,g,f,μ to be Robertson–Walker spacetime with Einstein fibers are derived. The Ricci tensor in this case gains the perfect fluid form. Likewise, it is proven that λ,n+m-Einstein M,g,w having harmonic Weyl tensor, ∇jw∇mwCjklm=0 and ∇lw∇lw<0 reduces fibers. Finally, if φ=−m∇lnw φRic-vector field on M an ψ=∇w ψRic-vector...

We investigate the particle-number fluctuations of condensate due to collective excitations for trapped two-dimensional (2D) and quasi-2D Bose gases at low temperature. We show that the fluctuations of the condensate are proportional to the square of the total particle number of the system. For a quasi-2D Bose gas the fluctuations are also proportional to the square root of the trapping frequen...

We consider the quasi-de Sitter geometry of the inflationary universe. We calculate the energy flux of the slowly rolling background scalar field through the quasi-de Sitter apparent horizon and set it equal to the change of the entropy (1/4 of the area) multiplied by the temperature, dE = TdS. Remarkably, this thermodynamic law reproduces the Friedmann equation for the rolling scalar field. Th...

Using effective formulas we analyze the Bose-Einstein correlations (BEC) data corrected for Coulomb interactions provided by STAR Collaboration and the quasi-corrected data on 2π and 3π BEC by using Coulomb wave function with coherence parameter included. The corresponding magnitudes of the interaction regions turn out to be almost the same: R Coul (2π) ≃ 3 2 R Coul (3π). Moreover, the genuine ...

Many authors have studied Ricci solitons and their analogs within the framework of (almost) contact geometry. In this article, we thoroughly study $$(m,\rho )$$ -quasi-Einstein structure on a metric manifold. First, prove that if K-contact or Sasakian manifold $$M^{2n+1}$$ admits closed structure, then it is an Einstein constant scalar curvature $$2n(2n+1)$$ , for particular case—a non-Sasak...