Phenomenological Analogy between Gross-Pitaevskii Theory for Bose-Einstein Condensate and Newton Equation for Classical Mechanics
Main Article Content
Abstract
In this work we found an interesting analogy between Gross-Pitaevskii theory for Bose-Einstein condensate at zero temperature and Newton equation of classical particle in the classical physics. Although this analogy is a pure phenomenology, it brings a new perspective to physics in general, in particular to quantum physics, as well as to many-body physics.
Keywords:
Bose-Einstein condensates, Gross-Pitaevskii equation, Newton equation, Phenomenological analogy.
References
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[3] M. H. Anderson, J. R. Ensher, M. R. Mathews, C. E. Wieman, E. A. Cornell, Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor, Science, Vol. 269, No. 5221, 1995, pp. 198-201, https://doi.org/10.1126/science.269.5221.198.
[4] A. Einstein, Quantentheorie Des Einatomigen Idealen Gases, Sitzungsberichte der Preussischen Akademie Der Wissenschaften, Vol. 22, No. 1, 1925, pp. 261-269.
[5] D. Halliday, R. Resnick, J. Walker, Fundamentals of Physics (12th Edition), Wiley Publisher, New York, 2003.
[6] K. B. Davis, M. O. Mewes, M. R. Andrews, N. J. V. Druten, D. S. Durfee, D. M. Kurn, W. Ketterle, Bose-Einstein Condensation in a Gas of Sodium Atoms, Phys. Rev. Lett., Vol. 75, No. 22, 1995, pp. 3969-3973, https://doi.org/10.1103/PhysRevLett.75.3969.
[7] P. S. Jessen, I. H. Deutsch, Optical Lattices, Opt. Lattices, Vol. 37, 1996, pp. 95-138, https://doi.org/10.1016/S1049-250X(08)60099-3.
[8] H. Denschlag, J. E. Simsarian, H. Haffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston,
W. D. Phillips, A Bose-Einstein Condensate in an Optical Lattice, J. Phys. B: At. Mol. Opt. Phys, Vol. 35, 2002, pp. 3095-3110, https://doi.org/10.1088/0953-4075/35/14/307.
[9] B. V. Schaeybroeck, J. O. Indekeu, Critical Wetting, First-Order Wetting, and Prewetting Phase Transitions in Binary Mixtures of Bose-Einstein condensates, Physical Review A, Vol. 91, No. 1, 2015, pp. 0136261-01362616, https://doi.org/10.1103/PhysRevA.91.013626.
[10] B. V. Schaeybroeck, P. Navez, J. O. Indekeu, Interface Potential and Line Tension for Bose-Einstein Condensate Mixtures Near A Hard Wall, Physical Review A, Vol. 105, No. 5, 2022, pp. 0533091-05330917, https://doi.org/10.1103/PhysRevA.105.053309.