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Use of Two-Body Correlated Basis Functions with van der Waals Interaction to Study the Shape-Independent Approximation for a Large Number of Trapped Interacting Bosons

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Abstract

We study the ground-state and the low-lying excitations of a trapped Bose gas in an isotropic harmonic potential for very small (\(\sim \)3) to very large (\(\sim \) \(10^7\)) particle numbers. We use the two-body correlated basis functions and the shape-dependent van der Waals interaction in our many-body calculations. We present an exhaustive study of the effect of inter-atomic correlations and the accuracy of the mean-field equations considering a wide range of particle numbers. We calculate the ground-state energy and the one-body density for different values of the van der Waals parameter \(C_{6}\). We compare our results with those of the modified Gross–Pitaevskii results, the correlated Hartree hypernetted-chain equations (which also utilize the two-body correlated basis functions), as well as of the diffusion Monte Carlo for hard sphere interactions. We observe the effect of the attractive tail of the van der Waals potential in the calculations of the one-body density over the truly repulsive zero-range potential as used in the Gross–Pitaevskii equation and discuss the finite-size effects. We also present the low-lying collective excitations which are well described by a hydrodynamic model in the large particle limit.

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Acknowledgements

BC acknowledges the financial support of Department of Science and Technology (DST), Government of India, under a Major Research Project [Sanc. No. SR/S2/CMP-126/2012].

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Authors and Affiliations

  1. Department of Physics, University of South Africa, P.O.Box 392, Pretoria, 0003, South Africa

    M. L. Lekala, B. Chakrabarti, G. J. Rampho & S. A. Sofianos

  2. Department of Physics, Presidency University, 86/1 College Street, Kolkata, 700 073, India

    B. Chakrabarti

  3. Department of Physics, University of Calcutta, 92 A.P.C. Road, Kolkata, 700084, India

    T. K. Das

  4. Square Kilometer Array Radiotelescope, The Park, Park Rd., Pinelands, 7405, South Africa

    R. M. Adam

  5. Theoretical Physics Division, Physical Research Laboratory, Navrangpura, Ahmendabad, 380 009, India

    S. K. Haldar

  6. Department of Physics, University of Haifa, Haifa, Israel

    S. K. Haldar

Authors
  1. M. L. Lekala
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  2. B. Chakrabarti
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  3. T. K. Das
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  4. G. J. Rampho
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  5. S. A. Sofianos
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  6. R. M. Adam
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  7. S. K. Haldar
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Corresponding author

Correspondence to G. J. Rampho.

Additional information

S. A. Sofianos—deceased.

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Lekala, M.L., Chakrabarti, B., Das, T.K. et al. Use of Two-Body Correlated Basis Functions with van der Waals Interaction to Study the Shape-Independent Approximation for a Large Number of Trapped Interacting Bosons. J Low Temp Phys 187, 232–250 (2017). https://doi.org/10.1007/s10909-016-1732-4

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  • DOI: https://doi.org/10.1007/s10909-016-1732-4

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