Incompressible energy spectrum from wave turbulence. (English) Zbl 1498.76045
Summary: Bose-Einstein condensates with their superfluidity property provide an interesting parallel to classical fluids. Due to the Kolmogorov spectrum of homogeneous turbulence the statistics of the incompressible velocity field is of great interest, but in superfluids obtaining quantities such as the statistics of the velocity field from the macroscopic wavefunction turns out be a complicated task; therefore, most of the work up to now has been numerical in nature. We made use of the Weak Wave Turbulence (WWT) theory, which provides the statistics of the macroscopic wavefunction, to obtain the statistics of the velocity field, which allowed us to produce a semi analytical procedure for extracting the incompressible energy spectrum in the WWT regime. This is done by introducing an auxiliary wavefunction that preserves the relevant statistical and hydrodynamical properties of the condensate but with a homogeneous density thus allowing for a simpler description of the velocity field.
MSC:
| 76F55 | Statistical turbulence modeling |
| 76A25 | Superfluids (classical aspects) |
| 82D50 | Statistical mechanics of superfluids |
Keywords:
Bose-Einstein condensate; superfluid; weak wave turbulence theory; macroscopic wavefunction statistics; velocity field statisticsReferences:
| [1] | Anderson, M. H.; Ensher, J. R.; Matthews, M. R.; Wieman, C. E.; Cornell, E. A., Observation of Bose-Einstein condensation in a dilute atomic vapor, Science, 269, 5221, 198-201 (1995) |
| [2] | Davis, K. B.; Mewes, M. O.; Andrews, M. R.; van Druten, N. J.; Durfee, D. S.; Kurn, D. M.; Ketterle, W., Bose-Einstein condensation in a gas of sodium atoms, Phys. Rev. Lett., 75, 22, 3969-3973 (1995) |
| [3] | Pethick, C.; Smith, H., Bose-Einstein Condensation in Dilute Gases (2008), Cambridge University Press: Cambridge University Press Cambridge ; New York |
| [4] | Bose-Einstein Condensation (1995), Cambridge University Press: Cambridge University Press Cambridge ; New York · Zbl 0835.62108 |
| [5] | Tsatsos, M. C.; Tavares, P. E.; Cidrim, A.; Fritsch, A. R.; Caracanhas, M. A.; dos Santos, F. E.A.; Barenghi, C. F.; Bagnato, V. S., Quantum turbulence in trapped atomic bose-Einstein condensates, Phys. Rep., 622, 1-52 (2016) |
| [6] | Barenghi, C.; Parker, N. G., (A Primer on Quantum Fluids. A Primer on Quantum Fluids, SpringerBriefs in Physics (2016), Springer International Publishing: Springer International Publishing Cham), arXiv:1605.09580 · Zbl 1345.82001 |
| [7] | Dalfovo, F.; Giorgini, S.; Pitaevskii, L. P.; Stringari, S., Theory of Bose-Einstein condensation in trapped gases, Rev. Modern Phys., 71, 3, 463-512 (1999), arXiv:cond-mat/9806038 |
| [8] | Madeira, L.; Cidrim, A.; Hemmerling, M.; Caracanhas, M. A.; dos Santos, F. E.A.; Bagnato, V. S., Quantum turbulence in Bose-Einstein condensates: present status and new challenges ahead, AVS Quantum Sci., 2, 3, Article 035901 pp. (2020) |
| [9] | Richardson, L. F., Atmospheric diffusion shown on a distance-neighbour graph, Proc. R. Soc. Lond. Ser. A Contain. Pap. Math. Phys. Charact., 110, 756, 709-737 (1926) |
| [10] | Leslie, D. C., Developments in the Theory of Turbulence (1973), Clarendon Press: Clarendon Press Oxford · Zbl 0273.76034 |
| [11] | McComb, W. D., (The Physics of Fluid Turbulence. The Physics of Fluid Turbulence, Oxford Engineering Science Series (2003), Clarendon Press [u.a.]: Clarendon Press [u.a.] Oxford) · Zbl 0748.76005 |
| [12] | Kolmogorov, A. N., The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Proc. R. Soc. Lond. Ser. A Math. Phys. Sci., 434, 1890, 9-13 (1991) · Zbl 1142.76389 |
| [13] | Frisch, U.; Kolmogorov, A. N., Turbulence: the Legacy of a. N. Kolmogorov (1995), Cambridge University Press · Zbl 0832.76001 |
| [14] | Kobayashi, M.; Tsubota, M., Kolmogorov spectrum of superfluid turbulence: numerical analysis of the Gross-Pitaevskii Equation with a small-scale dissipation, Phys. Rev. Lett., 94, 6, Article 065302 pp. (2005), arXiv:cond-mat/0411750 |
| [15] | Nore, C.; Abid, M.; Brachet, M. E., Kolmogorov turbulence in low-temperature superflows, Phys. Rev. Lett., 78, 20, 3896-3899 (1997) |
| [16] | Bradley, A. S.; Anderson, B. P., Energy spectra of vortex distributions in two-dimensional quantum turbulence, Phys. Rev. X, 2, 4, Article 041001 pp. (2012) |
| [17] | Cidrim, A.; White, A. C.; Allen, A. J.; Bagnato, V. S.; Barenghi, C. F., Vinen turbulence via the decay of multicharged vortices in trapped atomic Bose-Einstein condensates, Phys. Rev. A, 96, 2, Article 023617 pp. (2017) |
| [18] | Tsubota, M., Quantum turbulence, J. Phys. Soc. Japan, 77, 11, Article 111006 pp. (2008) |
| [19] | Baggaley, A. W.; Barenghi, C. F.; Sergeev, Y. A., Quasiclassical and ultraquantum decay of superfluid turbulence, Phys. Rev. B, 85, 6, 060501(r) (2012) |
| [20] | Zakharov, V. E.; L’vov, V. S.; Falkovich, G., (Calogero, F.; Fuchssteiner, B.; Rowlands, G.; Segur, H.; Wadati, M.; Zakharov, V. E., Kolmogorov Spectra of Turbulence I. Kolmogorov Spectra of Turbulence I, Springer Series in Nonlinear Dynamics (1992), Springer Berlin Heidelberg: Springer Berlin Heidelberg Berlin, Heidelberg) · Zbl 0786.76002 |
| [21] | Nazarenko, S., (Wave Turbulence. Wave Turbulence, Lecture Notes in Physics, vol. 825 (2011), Springer Berlin Heidelberg: Springer Berlin Heidelberg Berlin, Heidelberg) · Zbl 1220.76006 |
| [22] | Nazarenko, S., Wave turbulence, Contemp. Phys., 56, 3, 359-373 (2015) |
| [23] | Kolmakov, G. V.; McClintock, P. V.E.; Nazarenko, S. V., Wave turbulence in quantum fluids, Proc. Natl. Acad. Sci., 111, Supplement 1, 4727-4734 (2014) · Zbl 1355.76089 |
| [24] | Choi, Y.; Lvov, Y. V.; Nazarenko, S., Joint statistics of amplitudes and phases in wave turbulence, Physica D, 201, 1-2, 121-149 (2005), arXiv:math-ph/0412046 · Zbl 1143.76451 |
| [25] | Connaughton, C.; Josserand, C.; Picozzi, A.; Pomeau, Y.; Rica, S., Condensation of classical nonlinear waves, Phys. Rev. Lett., 95, 26, Article 263901 pp. (2005) |
| [26] | Fujimoto, K.; Tsubota, M., Bogoliubov-wave turbulence in bose-Einstein condensates, Phys. Rev. A, 91, 5 (2015) |
| [27] | Proment, D.; Nazarenko, S.; Onorato, M., Sustained turbulence in the three-dimensional Gross-Pitaevskii model, Physica D, 241, 3, 304-314 (2012) · Zbl 1457.76208 |
| [28] | Henn, E. A.L.; Seman, J. A.; Roati, G.; Magalhães, K. M.F.; Bagnato, V. S., Emergence of turbulence in an oscillating Bose-Einstein condensate, Phys. Rev. Lett., 103, 4, Article 045301 pp. (2009) |
| [29] | Thompson, K. J.; Bagnato, G. G.; Telles, G. D.; Caracanhas, M. A.; dos Santos, F. E.A.; Bagnato, V. S., Evidence of power law behavior in the momentum distribution of a turbulent trapped Bose-Einstein condensate, Laser Phys. Lett., 11, 1, Article 015501 pp. (2014) |
| [30] | Navon, N.; Gaunt, A. L.; Smith, R. P.; Hadzibabic, Z., Emergence of a turbulent cascade in a quantum gas, Nature, 539, 7627, 72-75 (2016) |
| [31] | Navon, N.; Eigen, C.; Zhang, J.; Lopes, R.; Gaunt, A. L.; Fujimoto, K.; Tsubota, M.; Smith, R. P.; Hadzibabic, Z., Synthetic dissipation and cascade fluxes in a turbulent quantum gas, Science, 366, 6463, 382-385 (2019), arXiv:1807.07564 |
| [32] | Proment, D.; Nazarenko, S.; Onorato, M., Energy cascades and spectra in turbulent Bose-Einstein condensates, Phys. Rev. A, 80, 5 (2009) |
| [33] | dos Santos, F. E.A., Hydrodynamics of vortices in Bose-Einstein condensates: A defect-gauge field approach, Phys. Rev. A, 94, 6, Article 063633 pp. (2016) |
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