A paper presents a theoretical investigation of subsonic and supersonic effects in a Bose-Einstein condensate (BEC). The BEC is represented by a time-dependent, nonlinear Schroedinger equation that includes terms for an external confining potential term and a weak interatomic repulsive potential proportional to the number density of atoms. From this model are derived Madelung equations, which relate the quantum phase with the number density, and which are used to represent excitations propagating through the BEC. These equations are shown to be analogous to the classical equations of flow of an inviscid, compressible fluid characterized by a speed of sound (g/ρ0)1/2, where g is the coefficient of the repulsive potential and ρ0 is the unperturbed mass density of the BEC. The equations are used to study the effects of a region of perturbation moving through the BEC. The excitations created by a perturbation moving at subsonic speed are found to be described by a Laplace equation and to propagate at infinite speed. For a supersonically moving perturbation, the excitations are found to be described by a wave equation and to propagate at finite speed inside a Mach cone.
This work was done by Michail Zak of Caltech for NASA's Jet Propulsion Laboratory. To obtain a copy of the paper, "Sub- and supersonic effects in Bose-Einstein condensate," access the Technical Support Package (TSP) free on-line at www.techbriefs.com/tsp under the Physical Sciences category. NPO-30637.
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Subsonic and Supersonic Effects in Bose-Einstein Condesate
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Overview
The document is a NASA Technical Support Package detailing research on subsonic and supersonic effects in Bose-Einstein condensates (BEC) and the impact of evaporating drops on turbulent flows. The study, conducted by Michail Zak and Igor K. Kulikov at the Jet Propulsion Laboratory, utilizes a time-dependent, nonlinear Schrödinger equation to model the BEC, incorporating external confining potentials and weak interatomic repulsive forces.
The research highlights the derivation of Madelung equations, which connect quantum phase with number density, drawing an analogy to classical fluid dynamics. These equations facilitate the analysis of excitations in the BEC, revealing that perturbations moving at subsonic speeds generate excitations described by a Laplace equation, propagating at infinite speed. Conversely, supersonic perturbations lead to excitations characterized by a wave equation, which propagate at finite speeds within a Mach cone.
Additionally, the document discusses a separate study on the effects of evaporating drops in turbulent flows. Direct numerical simulations were performed to analyze three mixing layers: one without drops and two with varying initial mass loadings of drops. The findings indicate that the presence of drops significantly alters turbulence dynamics. While drops reduce turbulence at large scales due to heating and evaporation, they increase turbulence at smaller scales. The study also identifies the contributions of chemical potential and viscosity to dissipation, noting that viscosity plays a lesser role in the presence of drops compared to other factors.
The document emphasizes the novelty of the research, particularly the discovery of new dynamical effects in BECs and the application of the Madelung description for high-density condensates. It aims to establish analogies between BEC behavior and classical gas dynamics, providing insights into the formation of sound barriers caused by moving profiles in the condensate.
Overall, this research contributes to a deeper understanding of quantum fluids and their behavior under various conditions, with potential applications in fields such as fluid dynamics, quantum mechanics, and materials science. The findings are set to be published in "Physics Letters A" in 2003, and further details can be accessed through the Technical Support Package online.
