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One dimensional Bose-Einstein condensate under the effect of the extended uncertainty principle

Published 21 Jul 2023 in cond-mat.quant-gas | (2307.11568v4)

Abstract: In this study, an analytical investigation was conducted to assess the effects of the extended uncertainty principle (EUP) on a Bose-Einstein condensate (BEC) described by the deformed one-dimensional Gross-Pitaevskii equation (GPE). Analytical solutions were derived for null potential while we used variational and numerical methods for a harmonic oscillator potential. The effects of EUP on stability, probability density, position, and momentum uncertainties of BEC are analyzed. The EUP is found to be applicable for the free dark soliton solution and in the presence of a harmonic potential within specific ranges of the deformation parameter $\alpha$, while it is not valid for the free bright soliton solution.

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References (44)
  1. Numerical solution of the gross–pitaevskii equation for bose–einstein condensation. Journal of Computational Physics, 187(1):318–342, 2003.
  2. Theory of bose-einstein condensation in trapped gases. Reviews of modern physics, 71(3):463, 1999.
  3. N Bogoliubov. On the theory of superfluidity. J. Phys, 11(1):23, 1947.
  4. Eugene P Gross. Hydrodynamics of a superfluid condensate. Journal of Mathematical Physics, 4(2):195–207, 1963.
  5. Lev P Pitaevskii. Vortex lines in an imperfect bose gas. Sov. Phys. JETP, 13(2):451–454, 1961.
  6. Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP, 34(1):62, 1972.
  7. Experimental observation of oscillating and interacting matter wave dark solitons. Physical review letters, 101(13):130401, 2008.
  8. Excitation modes of bright matter-wave solitons. Physical Review Letters, 123(12):123602, 2019.
  9. Scattering bright solitons: Quantum versus mean-field behavior. Physical Review A, 86(3):033608, 2012.
  10. Modulational instability and complex dynamics of confined matter-wave solitons. Physical review letters, 91(8):080405, 2003.
  11. Asymptotic generalized extended uncertainty principle. The European Physical Journal C, 80(7):676, 2020.
  12. JR Mureika. Extended uncertainty principle black holes. Physics Letters B, 789:88–92, 2019.
  13. Relativistic oscillators in new type of the extended uncertainty principle. International Journal of Modern Physics A, 34(32):1950218, 2019.
  14. The thermal properties of a two-dimensional dirac oscillator under an extended uncertainty principle: path integral treatment. The European Physical Journal Plus, 138(3):1–16, 2023.
  15. Pair creation in curved snyder space. International Journal of Modern Physics A, 35(04):2050014, 2020.
  16. The duffin-kemmer-petiau oscillator in the presence of minimal uncertainty in momentum. Physica Scripta, 95(7):075309, 2020.
  17. The eup dirac oscillator: A path integral approach. Few-Body Systems, 61(4):36, 2020.
  18. Extended uncertainty from first principles. Physics Letters B, 755:367–370, 2016.
  19. Modified inertia from extended uncertainty principle (s) and its relation to mond. The European Physical Journal C, 80:1–8, 2020.
  20. E Castellanos and JI Rivas. Planck-scale traces from the interference pattern of two bose-einstein condensates. Physical Review D, 91(8):084019, 2015.
  21. Nonextensive gross pitaevskii equation. International Journal of Geometric Methods in Modern Physics, 20(12):2350216–330, 2023.
  22. Frank Wilczek. Anyons. Scientific American, 264(5):58–65, 1991.
  23. Frank Wilczek. Disassembling anyons, 1992.
  24. Thermodynamic geometry of fractional statistics. Physical Review E, 82(3):031137, 2010.
  25. Bright soliton solution of a gross–pitaevskii equation. Applied Mathematics Letters, 26(7):718–724, 2013.
  26. Jesus Rogel-Salazar. The gross–pitaevskii equation and bose–einstein condensates. European Journal of Physics, 34(2):247, 2013.
  27. Salvatore Mignemi. Extended uncertainty principle and the geometry of (anti)-de sitter space. Modern Physics Letters A, 25(20):1697–1703, 2010.
  28. (anti-) de sitter black hole thermodynamics and the generalized uncertainty principle. General Relativity and Gravitation, 37:1255–1262, 2005.
  29. Analytical expressions for dark soliton solution of a gross–pitaevskii equation. Applied Mathematics and Computation, 273:383–389, 2016.
  30. Path integral in position-deformed heisenberg algebra with maximal length uncertainty. Annals of Physics, page 169389, 2023.
  31. Minimal length, maximal momentum, and hilbert space representation of quantum mechanics. Physical Review D, 85(10):104029, 2012.
  32. Numerical solution of the gross–pitaevskii equation for bose–einstein condensation. Journal of Computational Physics, 187(1):318–342, May 2003.
  33. Hayder Salman. A time-splitting pseudospectral method for the solution of the gross–pitaevskii equations using spherical harmonics with generalised-laguerre basis functions. Journal of Computational Physics, 258:185–207, February 2014.
  34. M. Caliari and S. Zuccher. Reliability of the time splitting fourier method for singular solutions in quantum fluids. Computer Physics Communications, 222:46–58, January 2018.
  35. Hanquan Wang. Numerical studies on the split-step finite difference method for nonlinear schrödinger equations. Applied Mathematics and Computation, 170(1):17–35, November 2005.
  36. Split-step fourier method for nonlinear schrodinger equation. In DAYS on DIFFRACTION 2006. IEEE, 2006.
  37. Higher-order split-step fourier schemes for the generalized nonlinear schrödinger equation. Mathematics and Computers in Simulation, 67(6):581–595, January 2005.
  38. Optimization of the split-step fourier method in modeling optical-fiber communications systems. Journal of Lightwave Technology, 21(1):61–68, January 2003.
  39. On the accuracy of split-step fourier simulations for wideband nonlinear optical communications. Journal of Lightwave Technology, 36(23):5669–5677, December 2018.
  40. Theory of bose-einstein condensation in trapped gases. Reviews of Modern Physics, 71(3):463–512, April 1999.
  41. Quantum fluctuations and condensate fraction during time-of-flight expansion. Physical Review A, 82(3), September 2010.
  42. C A Müller and C Gaul. Condensate deformation and quantum depletion of bose–einstein condensates in external potentials. New Journal of Physics, 14(7):075025, July 2012.
  43. Abdelâali Boudjemâa. Weakly interacting bose gases with generalized uncertainty principle: Effects of quantum gravity. The European Physical Journal Plus, 137(2), February 2022.
  44. Quantum depletion of a soliton condensate. Physics Letters A, 357(2):150–153, September 2006.
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