Resolving the puzzle of sound propagation in a dilute Bose–Einstein condensate

Abstract

A unified model of a dilute Bose–Einstein condensate is proposed, combining the logarithmic and Gross–Pitaevskii (GP) nonlinear terms in a wave equation, where the GP term describes two-body interactions, as suggested by the standard perturbation theory; while the logarithmic term is essentially nonperturbative, and takes into account quantum vacuum effects. The model is shown to have excellent agreement with sound propagation data in the condensate of cold sodium atoms known since the now classic works by Andrews and collaborators. The data also allowed us to place constraints on two of the unified model’s parameters, which describe the strengths of the logarithmic and GP terms. Additionally, we suggest an experiment constraining the value of the third parameter (the characteristic density scale of the logarithmic part of the model), using the conjectured attraction–repulsion transition of many-body interaction inside the condensate.

Can superfluid stars be mistaken for black holes in astronomical observations?

“…It should be emphasized that the potential in eq. ( 5) is the simplest possible one, because condensate equations for the quantum liquids we know of contain not only logarithmic but also polynomial nonlinear terms [17,19].…”

Derivation of Emergent Spacetime Metric, Gravitational Potential and Speed of Light in Superfluid Vacuum Theory

“…and O( f ) represents terms of order f . Same result can be obtained for a case of anisotropic logarithmic fluid by choosing a frame of reference aligned along the vector ∇b, such that ∇b = |∇b| n; then Equation ( 10) can be exactly integrated in the transverse directions to the normal n, hence we obtain p ⊥ = c 2 s ρ. Equations ( 11) and (12) indicate that our quantum Bose liquid behaves as an ideal fluid in the leading-order approximation, because c 2 s does not dependent on density. This feature originates from the logarithmic term in Equation ( 2), which makes logarithmic fluid models outstanding in their category.…”

“…In previous works on the theme, to mention the landmark works [7,8], we advocated a superfluid vacuum theory based on the assumption that the background superfluid belongs to a class of logarithmic fluid models. The latter have already found applications in modeling quantum Bose liquids produced in a laboratory, such as helium superfluids and Bose-Einstein condensates (BEC) of alkali atoms [9][10][11][12]. Moreover, those studies resulted in a strong intuitive feeling that the logarithmic models are a crucial ingredient and theoretical tool necessary for a consistent explanation/description of vacuum effects in laboratory quantum Bose liquids.…”

Sound Propagation in Cigar-Shaped Bose Liquids in the Thomas-Fermi Approximation: A Comparative Study between Gross-Pitaevskii and Logarithmic Models

“…A profound relation between logarithmic Schrödinger equations and quantum information entropy should be mentioned as well [19,20]. Fruitful applications of the logarithmic models were found in various physical systems [21][22][23][24][25][26][27][28][29][30][31][32]. Extensive mathematical studies of logarithmically nonlinear systems were performed as well, to mention only very recent results [33][34][35][36][37][38][39][40][41].…”