PHENOMENOLOGICAL ANALOGY BETWEEN GROSS-PITAEVSKII THEORY FOR BOSE--EINSTEIN CONDENSATE MIXTURES IN INFINITE SPACE AND CLASSICAL MECHANICS
DOI:
https://doi.org/10.18173/2354-1059.2025-0004Keywords:
Bose-Einstein condensate, Gross-Pitaevskii equations, Newton's equation of motion, Phenomenological analogyAbstract
Based on an analogy between the Gross-Pitaevskii (GP) equations for binary mixtures of Bose-Einstein condensates (BECs) at zero temperature and Newton’s equations of motion for a particle in a conservative field, we derive exact analytical solutions for the coupled GP equations in several phase-segregated BEC scenarios. In a straightforward manner, exact analytical solutions are obtained for both the symmetric and anti-symmetric cases. Furthermore, our approach enables us to propose approximate analytical solutions as an alternative to those derived from the widely used double-parabola approximation (DPA). Numerical computations demonstrate that our approximate solutions closely match the exact solutions within the GP framework. This finding is of particular significance for determining the wavefunctions of the condensates, a fundamental task in investigating the static properties of BECs.
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