No Access Published Online: 02 February 2016
Low Temperature Physics 42, 36 (2016); https://doi.org/10.1063/1.4939154
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An approach is proposed to obtain an effective Hamiltonian of a harmonically trapped Bose-system. Such a Hamiltonian is quadratic in the creation–annihilation operators and certain approximations allow to simplify higher (three and four operator) products to the required form. After the Hamiltonian diagonalization, the expression for the excitation spectrum is obtained containing in particular temperature-dependent corrections. Numerical calculations are made for a one-dimensional system. Some prospects towards the extension of the suggested approach to study binary bosonic mixtures are briefly discussed.
The paper is based on the research provided by the grant support of the State Fund for Fundamental Research of Ukraine, Project F-64/41-2015 (No. 0115U004838).
  1. 1. M. H. Anderson, J. N. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269, 198 (1995). https://doi.org/10.1126/science.269.5221.198, Google ScholarCrossref
  2. 2. K. B. Davis, M. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995). https://doi.org/10.1103/PhysRevLett.75.3969, Google ScholarCrossref
  3. 3. D. S. Jin, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. 77, 420 (1996). https://doi.org/10.1103/PhysRevLett.77.420, Google ScholarCrossref
  4. 4. S. Stringari, Phys. Rev. Lett. 77, 2360 (1996). https://doi.org/10.1103/PhysRevLett.77.2360, Google ScholarCrossref
  5. 5. L. You, W. Hoston, M. Lewenstein, and M. Marinescu, Acta Phys. Pol., A 93, 211 (1998). Google ScholarCrossref
  6. 6. S. Grossmann and M. Holthaus, Phys. Lett. A 208, 188 (1995). https://doi.org/10.1016/0375-9601(95)00766-V, Google ScholarCrossref
  7. 7. H. Haugerud, T. Haugset, and F. Ravndal, Phys. Lett. A 225, 18 (1997). https://doi.org/10.1016/S0375-9601(96)08842-1, Google ScholarCrossref
  8. 8. W. J. Mullin, J. Low Temp. Phys. 106, 615 (1997). https://doi.org/10.1007/BF02395928, Google ScholarCrossref
  9. 9. F. Gerbier, Europhys. Lett. 66, 771 (2004). https://doi.org/10.1209/epl/i2004-10035-7, Google ScholarCrossref
  10. 10. A. S. Parkins and D. F. Walls, Phys. Rep. 303, 1 (1998). https://doi.org/10.1016/S0370-1573(98)00014-3, Google ScholarCrossref
  11. 11. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 71, 463 (1999). https://doi.org/10.1103/RevModPhys.71.463, Google ScholarCrossref
  12. 12. I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80, 885 (2008). https://doi.org/10.1103/RevModPhys.80.885, Google ScholarCrossref
  13. 13. V. S. Bagnato, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and D. Mihalache, Rom. Rep. Phys. 67, 5 (2015). Google Scholar
  14. 14. C. Menotti and S. Stringari, Phys. Rev. A 66, 043610 (2002). https://doi.org/10.1103/PhysRevA.66.043610, Google ScholarCrossref
  15. 15. Y.-W. Luo and J.-S. Chen, Commun. Theor. Phys. 60, 673 (2013). https://doi.org/10.1088/0253-6102/60/6/07, Google ScholarCrossref
  16. 16. K. R. A. Hazzard and E. J. Mueller, Phys. Rev. A 76, 063612 (2007). https://doi.org/10.1103/PhysRevA.76.063612, Google ScholarCrossref
  17. 17. M. Yamashita, S. Kato, A. Yamaguchi, S. Sugawa, T. Fukuhara, S. Uetake, and Y. Takahashi, Phys. Rev. A 87, 041604(R) (2013). https://doi.org/10.1103/PhysRevA.87.041604, Google ScholarCrossref
  18. 18. I. V. Stasyuk, O. V. Velychko, and I. R. Dulepa, Ukr. J. Phys. 59, 993 (2014). https://doi.org/10.15407/ujpe59.10.0993, Google ScholarCrossref
  19. 19. N. N. Bogoliubov, J. Phys. (USSR) 11, 23 (1947). Google Scholar
  20. 20. P. Grech and R. Seiringer, Commun. Math. Phys. 322, 559 (2013). https://doi.org/10.1007/s00220-013-1736-8, Google ScholarCrossref
  21. 21. R. Seiringer, J. Math. Phys. 55, 075209 (2014). https://doi.org/10.1063/1.4881536, Google ScholarScitation
  22. 22. C. Trallero-Giner, M. V. Durnev, Y. Núñez Fernández, M. I. Vasilevskiy, V. López-Richard, and A. Kavokin, Phys. Rev. B 89, 205317 (2014). https://doi.org/10.1103/PhysRevB.89.205317, Google ScholarCrossref
  23. 23. V. I. Yukalov and H. Kleinert, Phys. Rev. A 73, 063612 (2006). https://doi.org/10.1103/PhysRevA.73.063612, Google ScholarCrossref
  24. 24. T. Ernst, T. Paul, and P. Schlagheck, Phys. Rev. A 81, 013631 (2010). https://doi.org/10.1103/PhysRevA.81.013631, Google ScholarCrossref
  25. 25. V. I. Yukalov, E. P. Yukalova, and V. S. Bagnato, Laser Phys. 19, 686 (2009). https://doi.org/10.1134/S1054660X09040240, Google ScholarCrossref
  26. 26. V. I. Yukalov, Phys. Part. Nucl. 42, 460 (2011). https://doi.org/10.1134/S1063779611030063, Google ScholarCrossref
  27. 27. N. Argaman and Y. B. Band, Phys. Rev. A 83, 023612 (2011). https://doi.org/10.1103/PhysRevA.83.023612, Google ScholarCrossref
  28. 28. A. Alastuey and J. Piasecki, Phys. Rev. E 84, 041122 (2011). https://doi.org/10.1103/PhysRevE.84.041122, Google ScholarCrossref
  29. 29. H. Kim, C. S. Kim, C. L. Huang, H.-S. Song, and X.-X. Yi, Phys. Rev. A 85, 033611 (2012). https://doi.org/10.1103/PhysRevA.85.033611, Google ScholarCrossref
  30. 30. H. Kim, C.-S. Kim, C.-L. Huang, H.-S. Song, and X.-X. Yi, Phys. Rev. A 85, 053629 (2012). https://doi.org/10.1103/PhysRevA.85.053629, Google ScholarCrossref
  31. 31. A. Roy and D. Angom, Phys. Rev. A 92, 011601 (2015). https://doi.org/10.1103/PhysRevA.92.011601, Google ScholarCrossref
  32. 32. X.-L. Chen, Y. Li, and H. Hu, Phys. Rev. A 91, 063631 (2015). https://doi.org/10.1103/PhysRevA.91.063631, Google ScholarCrossref
  33. 33. A. A. Rovenchak, J. Low Temp. Phys. 148, 411 (2007). https://doi.org/10.1007/s10909-007-9406-x, Google ScholarCrossref
  34. 34. J. H. P. Colpa, Physica A 93, 327 (1978). https://doi.org/10.1016/0378-4371(78)90160-7, Google ScholarCrossref
  35. 35. C. Tsallis, J. Math. Phys. 19, 277 (1978). https://doi.org/10.1063/1.523549, Google ScholarScitation
  36. 36. M. Marinescu and A. F. Starace, Phys. Rev. A 56, 570 (1997). https://doi.org/10.1103/PhysRevA.56.570, Google ScholarCrossref
  37. 37. A. Rovenchak, Z. Naturforsch., A 70, 73 (2015). Google ScholarCrossref
  38. 38. E. C. Titchmarsh, J. London Math. Soc. s1-23, 15 (1949). Google ScholarCrossref
  39. 39. R. D. Lord, J. London Math. Soc. s1-24, 101 (1949). https://doi.org/10.1112/jlms/s1-24.2.101, Google ScholarCrossref
  40. 40. S. D. Bajpai, Ann. Math. Silesiensis 6, 13 (1992). Google Scholar
  41. 41. S. Giorgini, L. P. Pitaevskii, and S. Stringari, Phys. Rev. A 54, R4633 (1996). https://doi.org/10.1103/PhysRevA.54.R4633, Google ScholarCrossref
  42. 42. K. Kasamatsu and M. Tsubota, J. Low Temp. Phys. 150, 599 (2008). https://doi.org/10.1007/s10909-007-9600-x, Google ScholarCrossref
  43. 43. R. Campbell, G.-L. Oppo, and M. Borkowski, Phys. Rev. E 91, 012909 (2015). https://doi.org/10.1103/PhysRevE.91.012909, Google ScholarCrossref
  44. 44. B. Pasquiou, A. Bayerle, S. M. Tzanova, S. Stellmer, J. Szczepkowski, M. Parigger, R. Grimm, and F. Schreck, Phys. Rev. A 88, 023601 (2013). https://doi.org/10.1103/PhysRevA.88.023601, Google ScholarCrossref
  45. 45. B. Van Schaeybroeck, Physica A 392, 3806 (2013). https://doi.org/10.1016/j.physa.2013.04.026, Google ScholarCrossref
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