A paper presents a theoretical study of shock waves in a trapped Bose-Einstein condensate (BEC).
The mathematical model of the BEC in this study is a nonlinear Schroedinger equation (NLSE) in which (1) the role of the wave function of a single particle in the traditional Schroedinger equation is played by a space- and time-dependent complex order parameter ?(x,t) proportional to the square root of the density of atoms and (2) the atoms engage in a repulsive interaction characterized by a potential proportional to | ?(x,t)|2. Equations that describe macroscopic perturbations of the BEC at zero temperature are derived from the NLSE and simplifying assumptions are made, leading to equations for the propagation of sound waves and the transformation of sound waves into shock waves. Equations for the speeds of shock waves and the relationships between jumps of velocity and density across shock fronts are derived. Similarities and differences between this theory and the classical theory of sound waves and shocks in ordinary gases are noted. The present theory is illustrated by solving the equations for the example of a shock wave propagating in a cigar-shaped BEC.
This work was done by Igor Kulikov and Michail Zak of Caltech for NASA's Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com/tsp under the Physical Sciences category.
NPO-30593.
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Shock Waves in a Bose-Einstein Condensate
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Overview
The document is a Technical Support Package from NASA, specifically focusing on "Shock Waves in a Bose-Einstein Condensate" (BEC). It is part of the NASA Tech Briefs, which disseminate information on aerospace-related developments that have potential technological, scientific, or commercial applications. The document is identified as NPO-30593 and is provided under the Commercial Technology Program of NASA.
Bose-Einstein Condensates are states of matter formed at temperatures close to absolute zero, where a group of atoms behaves as a single quantum entity. The study of shock waves in BECs is significant because it can lead to a deeper understanding of quantum mechanics and the behavior of matter under extreme conditions. This research has implications for various fields, including condensed matter physics, quantum computing, and materials science.
The document emphasizes the importance of making research findings accessible to a broader audience, including industries and researchers outside of NASA. It highlights the potential for these findings to influence technological advancements and innovations. The Technical Support Package serves as a resource for those interested in the applications of shock wave phenomena in BECs, providing insights into experimental methods, theoretical frameworks, and potential applications.
Additionally, the document includes contact information for the NASA Scientific and Technical Information (STI) Program Office, which offers further assistance and access to a variety of publications related to aerospace research and technology. The STI Program Office can be reached through their website or directly via phone, fax, or email.
The document also includes a disclaimer stating that the United States Government and its representatives do not assume liability for the use of the information contained within, nor do they guarantee that such use will be free from privately owned rights. The mention of trade names or manufacturers is for identification purposes only and does not imply official endorsement by NASA.
In summary, this Technical Support Package provides valuable insights into the study of shock waves in Bose-Einstein Condensates, emphasizing the significance of this research in advancing scientific knowledge and its potential applications across various fields.
