Dependence of the Bose-Condensate Population Fluctuations in a Gas of Interacting Particles on the System Size: Numerical Analysis

We consider the Bose-condensate population statistics for a gas of interacting particles confined into a three-dimensional cubic trap with different boundary conditions at a low temperature. Behavior of the mathematical expectation and variance of the condensate population with the system size increase corresponding to the transition to a thermodynamic limit at constant temperature and density of the gas is examined on the basis of numerical calculations. A competition between the thermal and quantum contributions to the moments of the statistical distribution, as well as the dependence of the statistics character on the boundary conditions, are analyzed for a wide range of trap sizes corresponding to the actual experiments. We estimate with what accuracy and starting with which system sizes the thermodynamic-limit results could be applied to the actual mesoscopic systems.

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References

  1. 1.

    M. Kristensen, M. Christensen, M. Gajdacz, et al., Phys. Rev. Lett., 122, No. 16, 163601 (2019). https://doi.org/https://doi.org/10.1103/PhysRevLett.122.163601

  2. 2.

    M. Mehboudi, A. Lampo, C. Charalambous, et al., Phys. Rev. Lett., 122, No. 3, 030403 (2019). https://doi.org/https://doi.org/10.1103/PhysRevLett.122.030403

  3. 3.

    R. Lopes, C. Eigen, N. Navon, et al., Phys. Rev. Lett., 119, No. 19, 190404 (2017). https://doi.org/https://doi.org/10.1103/PhysRevLett.119.190404

  4. 4.

    L. Chomaz, L. Corman, T. Bienaimé, et al., Nat. Commun., 6, No. 1, 6162 (2015). https://doi.org/https://doi.org/10.1038/ncomms7162

  5. 5.

    A. Perrin, R. Bücker, S. Manz, et al., Nat. Phys., 8, No. 3, 195–198 (2912). https://doi.org/https://doi.org/10.1038/nphys2212

  6. 6.

    L.D. Landau and E. M. Lifshitz, Statistical Physics, Part 2 Butterworth–Heinemann, Oxford (1995).

  7. 7.

    W. Zwerger, Phys. Rev. Lett ., 92, No. 2, 027203 (2004). https://doi.org/https://doi.org/10.1103/PhysRevLett.92.027203

  8. 8.

    L. Pitaevskii and S. Stringari, Bose–Einstein Condensation and Superfluidity, Oxford University Press, Oxford (2016), Vol. 164.

  9. 9.

    C. J. Pethick and H. Smith, Bose–Einstein Condensation in Dilute Gases, Cambridge University Press, Cambridge (2002).

    Google Scholar 

  10. 10.

    V. V. Kocharovsky and Vl. V. Kocharovsky, Physica Scripta, 90, No. 10, 108002 (2015). https://doi.org/https://doi.org/10.1088/0031-8949/90/10/108002

  11. 11.

    N. Bogoliubov, J. Phys., 11, No. 1, 23–32 (1947).

    Google Scholar 

  12. 12.

    H. Shi and A. Griffin, Phys. Rep., 304, Nos. 1–2, 1–87 (1998). https://doi.org/https://doi.org/10.1016/S0370-1573(98)00015-5

  13. 13.

    S. V. Tarasov, Vl. V. Kocharovsky, and V. V. Kocharovsky, Radiophys. Quantum Electron., 62, No. 4, 293–310 (2019). https://doi.org/https://doi.org/10.1007/s11141-019-09978-7

  14. 14.

    S. Giorgini, L. Pitaevskii, and S. Stringari, Phys. Rev. Lett ., 80, No. 23, 5040–5043 (2998). https://doi.org/https://doi.org/10.1103/PhysRevLett.80.5040\

  15. 15.

    V. V. Kocharovsky, Vl. V. Kocharovsky, and M.O. Scully, Phys. Rev. A, 61, No. 5, 053606 (2000). https://doi.org/https://doi.org/10.1103/PhysRevA.61.053606

  16. 16.

    S. V. Tarasov, Vl. V. Kocharovsky, and V.V.Kocharovsky, Entropy, 20, No. 3, 153 (2018). https://doi.org/https://doi.org/10.3390/e20030153

  17. 17.

    S. V. Tarasov, Vl. V. Kocharovsky, and V.V.Kocharovsky, Phys. Rev. A, 90, No. 3, 033605 (2014). https://doi.org/https://doi.org/10.1103/PhysRevA.90.033605

  18. 18.

    S. Giorgini, J. Boronat, and J. Casulleras, Phys. Rev. A. Phys. Rev. A, 60, No. 6, 5129–5132 (1999). https://doi.org/https://doi.org/10.1103/PhysRevA.60.5129

  19. 19.

    T. D. Lee, K. Huang, and C.N.Yang, Phys. Rev., 106, No. 6, 1135–1145 (1957). https://doi.org/https://doi.org/10.1103/PhysRev.106.1135

  20. 20.

    P. Fedichev and G. Shlyapnikov, Phys. Rev. A, 58, No. 4, 3146–3158 (1998). https://doi.org/https://doi.org/10.1103/PhysRevA.58.3146

  21. 21.

    J. O. Andersen, Rev. Mod. Phys., 76, No. 2, 599–638 (2004). https://doi.org/https://doi.org/10.1103/RevModPhys.76.599

  22. 22.

    N.P. Proukakis and B. Jackson, J. Phys. B. At. Mol. Opt., 41, No. 20, 203002 (2008). https://doi.org/https://doi.org/10.1088/0953-4075/41/20/203002

  23. 23.

    S. Bhattacharyya and B. Chakrabarti, Phys. Rev. A, 93, No. 2, 023636 (2016). https://doi.org/https://doi.org/10.1103/PhysRevA.93.023636

  24. 24.

    S. Chatterjee and P. Diaconis, J. Phys. A. Math. Theor., 47, No. 8, 085201 (2014). https://doi.org/https://doi.org/10.1088/1751-8113/47/8/085201

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Correspondence to S. V. Tarasov.

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 63, No. 4, pp. 319–329, April 2020.

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Tarasov, S.V., Kocharovsky, V.V. & Kocharovsky, V.V. Dependence of the Bose-Condensate Population Fluctuations in a Gas of Interacting Particles on the System Size: Numerical Analysis. Radiophys Quantum El 63, 288–297 (2020). https://doi.org/10.1007/s11141-021-10053-3

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