| Feynman, R. P., Leighton R. B., and Sands M., The Feynman Lectures on Physics, Addison-Wesley, San Francisco, 2006. | |
| Pethick, C. J. and Smith, H., Bose-Einstein Condensation in Dilute Gases, Cambridge University Press, Cambridge, 2002. | |
| Tilley, D. R. and Tilley, J., Superfluidity and Superconductivity, 3rd edn., Institute of Physics Publishing, Bristol and Philadelphia, 1990. | |
| Feynman, R. P., Application of quantum mechanics to liquid helium, in: Gorter, C. J., ed., Prog. Low Temp. Phys., North-Holland, Amsterdam, 1955, Vol. I, 17-53. | |
| Vinen, W. F., The detection of a single quantum of circulation in liquid helium II, Proc. Roy. Soc. A, 1958, 260, 400-413. | |
| Gorter, C. J. and Mellink, J. H., On the irreversible processes in liquid helium II, Physica, 1949, 15, 285-304. CrossRef | |
| Vinen, W. F., Mutual friction in a heat current in liquid helium II: I. Experiments on steady heat currents, Proc. Roy. Soc. A, 1957, 240, 114-127. CrossRef | |
| Vinen, W. F., Mutual friction in a heat current in liquid helium II: II. Experiments on transient effects, Proc. Roy. Soc. A, 1957, 240, 128-143. CrossRef | |
| Vinen, W. F., Mutual friction in a heat current in liquid helium II: III. Theory of the mutual friction, Proc. Roy. Soc. A, 1957, 242, 493-515. CrossRef | |
| Vinen, W. F., Mutual friction in a heat current in liquid helium II: IV Critical heat currents in wide channels, Proc. Roy. Soc. A, 1958, 243, 400-413. CrossRef | |
| Tough, J. T., Superfluid turbulence, in: Gorter, C. J., ed., Prog. Low Temp. Phys., North-Holland, Amsterdam, 1982, Vol. VIII, 133-220. | |
| Schwarz, K. W., Three-dimensional vortex dynamics in superfluid 4He: Line-line and line-boundary interactions, Phys. Rev. B, 1985, 31, 5782-5803. CrossRef | |
| Schwarz, K. W., Three-dimensional vortex dynamics in superfluid 4He: Homogenous superfluid turbulence, Phys. Rev. B, 1988, 38, 2398-2417. CrossRef | |
| Frisch, U., Turbulence, Cambridge University Press, Cambridge, 1995. | |
| Kolmogorov, A. N., The local structure of turbulence in incompressible viscous fluid for very large Reynolds number, Dokl. Akad. Nauk SSSR, 1941, 30, 299-303 [reprinted in Proc. Roy. Soc. A, 1991, 434, 9-13]. | |
| Kolmogorov, A. N., On degeneration (decay) of isotropic turbulence in an incompressible viscous liquid, Dokl. Akad. Nauk SSSR, 1941, 31, 538-540 [reprinted in Proc. Roy. Soc. A, 1991, 434, 15-17]. | |
| Vinen, W. F. and Niemela, J. J., Quantum turbulence, J. Low Temp. Phys., 2002, 128, 167-231. CrossRef | |
| Vinen, W. F., An introduction to quantum turbulence, J. Low Temp. Phys., 2006, 145, 7-24. CrossRef | |
| Halperin, W. P. and Tsubota, M., ed., Prog. Low Temp. Phys., Elsevier, Amsterdam, 2008, Vol. 16. | |
| Tsubota, M., Quantum turbulence, J. Phys. Soc. Jpn., 2008, 78, 111006. | |
| Tsubota, M., Quantum turbulence, Contemporary Physics, 2009, 50, 463-475. CrossRef | |
| Kasamatsu, K. and Tsubota, M., Quantized vortices in atomic Bose-Einstein condensates, in: Halperin, W. P. and Tsubota, M., ed., Prog. Low Temp. Phys., Elsevier, Amsterdam, 2008, Vol.16, 351-403. | |
| Abo-Shaeer, J. R., Raman, C., Vogels, M. and Ketterle, W., Observation of vortex lattices in Bose-Einstein condensates, Science, 2001, 292, 476-479. CrossRef | |
| Madison, K. W., Chevy, F., Wlhlleben, W. and Dalibard, J., Vortex formation in a stirred Bose-Einstein condensate, Phys. Rev. Lett., 2000, 84, 806-809. CrossRef | |
| Madison, K. W., Chevy, F., Wlhlleben, W. and Dalibard, J, Statonary states of a rotating Bose-Einstein condensate: Routes to vortex nucleation, Phys. Rev. Lett., 2001, 86, 4443-4446. CrossRef | |
| Saffman P. G., Vortex Dynamics, Cambridge University Press, Cambridge, 1992. | |
| Tsubota, M., Araki, T. and Nemirovskii, S. K., Dynamics of vortex tangle without mutual friction in superfluid 4He, Phys. Rev. B, 2000, 62, 11751-11762. CrossRef | |
| Koplik, J. and Levine, H., Vortex reconnection in superfluid helium, Phys. Rev. Lett., 1993, 71, 1375-1378. CrossRef | |
| Leadbeater, M., Winiecki, T., Samuels, D. C., Barenghi, C. F. and Adams, C. S., Sound emission due to superfluid vortex reconnections, Phys. Rev. Lett., 2001, 86, 1410-1413. CrossRef | |
| Ogawa, S., Tsubota, M. and Hattori, Y., Study of reconnection and acoustic emission of quantized vortices in superfluid by the numerical analysis of the Gross-Pitaevskii equation, J. Phys. Soc. Jpn., 2002, 71, 813-821. CrossRef | |
| Williams, G. A. and Packard, R. E., Photographs of quantized vortex lines in rotating He II, Phys. Rev. Lett., 1974, 33, 280-283. CrossRef | |
| Yarmchuck, E. J. and Packard, R. E., Photographic studies of quantized vortex lines, J. Low Temp. Phys., 1982, 46, 479-515. CrossRef | |
| Matthews, M. R., Anderson, B. P., Haljan, P. C., Hall, D. S., Wieman, C. E. and Cornell, E. A., Vortices in a Bose-Einstein condensate, Phys. Rev. Lett., 1999, 83, 2498-2501. CrossRef | |
| Tsubota, M., Kasamatsu, K. and Ueda, M., Vortex lattice formation in a rotating Bose-Einstein condensate, Phys. Rev. A, 202, 65, 023603. | |
| Kasamatsu, K., Tsubota M. and Ueda M., Nonlinear dynamics of vortex lattice formation in a rotating Bose-Einstein condensate, Phys. Rev. A, 2003, 67, 033610. CrossRef | |
| Kasamatsu, K., Machida, M., Sasa, N. and Tsubota, M., Three-dimensional dynamics of vortex-lattice formation in Bose-Einstein condensate, Phys. Rev. A, 2005, 71, 063616. CrossRef | |
| Maurer, J. and Tabeling, P., Local investigation of superfluid turbulence, Europhys. Lett., 1998, 43, 29-34. CrossRef | |
| Stalp, S. R., Skrbek, L. and Donnelly, R. J., Decay of grid turbulence in a finite channel, Phys. Rev. Lett., 1999, 82, 4831-4834. CrossRef | |
| Skrbek, L., Niemela, J. J. and Donnelly, R. J., Four regimes of decaying grid turbulence in a finite channel, Phys. Rev. Lett., 2000, 85, 2973-2976. CrossRef | |
| Skrbek, L. and Stalp, S. R., On the decay of homogeneous isotropic turbulence, Phys. Fluids, 1997, 12, 1997-2019. CrossRef | |
| Stalp, S. R., Niemela, J. J., Vinen, W. F. and Donnelly, R. J., Dissipation of grid turbulence in helium II, Phys. Fluids, 2002, 14, 1377-1379. | |
| Hinze, J. O., Turbulence, 2nd edn., McGraw Hill, New York, 1975. | |
| Vinen, W. F., Classical character of turbulence in a quantum liquid, Phys. Rev. B, 2000, 61, 1410-1420. CrossRef | |
| Walmsley, P. M., Golov, A. I., Hall, H. E., Levchenko, A. A. and Vinen, W. F., Dissipation of quantum turbulence in the zero temperature limit, Phys. Rev. Lett., 2007, 99, 265302. CrossRef | |
| Bradley, D. I., Clubb, D. O., Fisher, S. N., Guenault, A. M., Halay, R. P., Matthews, C. J., Pickett, G. R., Tsepelin, V. and Zaki, K., Decay of pure quantum turbulence in superfluid 3He-B, Phys. Rev. Lett., 2006, 96, 035301. CrossRef | |
| Fisher, S. N. and Pickett, G. R., Quantized turbulence in superfluid 3He at very low temperatures, in: Halperin, W. P. and Tsubota, M., ed., Prog. Low Temp. Phys., Elsevier, Amsterdam, 2008, Vol. 16, 147-194. | |
| L'vov, V. S., Nazarenko, S. V. and Skrbek, L., Energy spectra of developed turbulence in helium superfluids, J. Low Temp. Phys., 2006, 145, 125-142. CrossRef | |
| Tsubota, M. and Kobayashi, M., Energy spectra of quantum turbulence, in: Halperin, W. P. and Tsubota, M., ed., Prog. Low Temp. Phys., Elsevier, Amsterdam, 2008, Vol. 16, 1-43. | |
| Skrbek, L. and Vinen, W. F., The use of vibrating structures in the study of quantum turbulence, in: Halperin, W. P. and Tsubota, M., ed., Prog. Low Temp. Phys., Elsevier, Amsterdam, 2008, Vol. 16, 195-246. | |
| Van Sciver, S. W. and Barenghi, C. F., Visualization of quantum turbulence, in: Halperin, W. P. and Tsubota, M., ed., Prog. Low Temp. Phys., Elsevier, Amsterdam, 2008, Vol. 16, 247-304. | |
| Nore, C., Abid, M. and Brachet, M. E., Kolmogorov turbulence in low-temperature superflows, Phys. Rev. Lett., 1997, 78, 3296-3299. | |
| Nore, C., Abid, M. and Brachet, M. E., Decaying Kolmogorov turbulence in a model of superflow, Phys. Fluids, 1997, 9, 2644-2669. CrossRef | |
| Araki, T., Tsubota, M. and Nemirovskii, S. K., Energy spectrum of superfluid turbulence with no normal-fluid component, Phys. Rev. Lett., 2002, 89, 145301. CrossRef | |
| Kobayashi, M. and Tsubota, M., Kolmogorov spectrum of superfluid turbulence: Numerical analysis of the Gross-Pitaevskii equation with a small-scale dissipation, Phys. Rev. Lett., 2005, 94, 065302. CrossRef | |
| Kobayashi, M. and Tsubota, M., Kolmogorov spectrum of quantum turbulence, J. Phys. Soc. Jpn., 2005, 74, 3248-3258. CrossRef | |
| Kobayashi, M. and Tsubota, M., Thermal dissipation in quantum turbulence, Phys. Rev. Lett., 2006, 97, 145301. CrossRef | |
| Kobayashi, M. and Tsubota, M., Decay of quantized vortices in quantum turbulence, J. Low Temp. Phys., 2006, 145, 209-218. CrossRef | |
| Thomson, J., Vibrations of a columnar vortex, Phil Mag., 1880, 10, 155-168. CrossRef | |
| Hall, H. E., An experimental and theoretical study of torsional oscillations in uniformly rotating liquid helium II, Proc. Roy. Soc. London A, 1958, 245, 546-561. CrossRef | |
| Hall, H. E., The rotation of helium II, Phil. Mag. Suppl., 1960, 9, 89-146. | |
| Vinen, W. F., Decay of superfluid turbulence at a very low temperature: The radiation of sound from a Kelvin wave on a quantized vortex, Phys. Rev. B, 2001, 64, 134520. CrossRef | |
| Samuels, D. C. and Donnelly, R. J., Sideband instability and recurrence of Kelvin waves on vortex cores, Phys. Rev. Lett., 1990, 64, 1385-1388. CrossRef | |
| Svistunov, B. V., Superfluid turbulence in the low-temperature limit, Phys. Rev. B, 1995, 52, 3647-3653. CrossRef | |
| Kivotides, D., Vassilicos, J. C., Samuels, D. C. and Barenghi, C. F., Kelvin waves cascade in superfluid turbulence, Phys. Rev. Lett., 2001, 86, 3080-3083. CrossRef | |
| Vinen, W. F., Tsubota, M. and Mitani, A., Kelvin-wave cascade on a vortex in superfluid 4He at a very low temperature, Phys. Rev. Lett., 2003, 91, 135301. CrossRef | |
| Kozik, E. and Svistunov, B. V., Kelvin-wave cascade and decay of superfluid turbulence, Phys. Rev. Lett., 2004, 92, 035301. CrossRef | |
| Kozik, E. and Svistunov, B. V., Scale-separation scheme for simulating superfluid turbulence: Kelvin-wave cascade, Phys. Rev. Lett., 2005, 94, 025301. CrossRef | |
| Kozik, E. and Svistunov, B. V., Vortex-phonon interaction, Phys. Rev. B, 2005, 72, 172505. CrossRef | |
| L'vov, V. S., Nazarenko, S. V. and Rudenko, O., Bottleneck crossover between classical and quantum superfluid turbulence, Phys. Rev. B, 2007, 76, 024520. CrossRef | |
| Kozik, E. and Svistunov, B. V., Kolmogorov and Kelvin-wave cascades of superfluid turbulence at T = 0: What lies between, Phys. Rev. B, 2008, 77, 060502. CrossRef | |
| Kozik, E. and Svistunov, B. V., Scanning superfluid-turbulence cascade by its low-temperature cutoff, Phys. Rev. Lett., 2008, 100, 195302. CrossRef | |
| Cannaughtoni, C. and Nazarenko, S. V., Warm cascades and anomalous scaling in a diffusion model of turbulence, Phys. Rev. Lett, 2004, 92, 044501. CrossRef | |
| Walmsley, P. M. and Golov, A. I., Quantum and quasiclassical types of superfluid turbulence, Phys. Rev. Lett., 2008, 100, 245301. CrossRef | |
| Tsubota, M., Araki T. and Vinen, W. F., Diffusion of an inhomogeneous vortex tangle, Physica B, 2003, 329-333, 224-225. CrossRef | |
| Finne, A. P., Eltsov, V. B., Hänninen, R., Kopnin, N. B., Kopu, J., Krusius, M., Tsubota, M. and Volovik, G. E., Dynamics of vortices and interfaces in superfluid 3He, Rep. Progr. Phys., 2006, 69, 3157-3230. CrossRef | |
| Eltsov, V. B., de Graaf, R., Hänninen, R., Krusius, K., Solntsev, R. E, L'vov, V. S., Golov, A. I. and Walmsley, P. M., Turbulent dynamics in rotating helium superfluids, in: Halperin, W. P. and Tsubota, M., ed., Prog. Low Temp. Phys., Elsevier, Amsterdam, 2008, Vol. 16, 45-146. | |
| Finne, A. P., Araki, T., Blaauwgeers, R., Eltsov, V. B., Kopnin, N. B., Krusius, M., Skrbek, L., Tsubota, M. and Volovik, G. E., An intrinsic velocity-independent criterion for superfluid turbulence, Nature, 2003, 424, 1022-1025. CrossRef | |
| Finne, A. P., Boldarev, R., Eltsov, V. B. and Krusius, M., Measurement of turbulence in superfluid 3He-B, J. Low Temp. Phys., 2004, 136, 249-279. CrossRef | |
| Finne, A. P., Eltsov, V. B., Eska, G., Hänninen, R., Kopu, J., Krusius, M., Thuneberg, E. V. and Tsubota, M., Vortex multiplication in applied flow: a precursor to superfluid turbulence, Phys. Rev. Lett., 2006, 96, 085301. CrossRef | |
| Eltsov, V. B., Finne, A. P., Hänninen, R., Kopu, J., Krusius, M., Tsubota, M. and Thuneberg, E. V., Twisted vortex state, Phys. Rev. Lett., 2006, 96, 215302. CrossRef | |
| Eltsov, V. B., Golov, A. I., de Graaf, R., Hänninen, R., Krusius, M., L'vov, V. S. and Solntsev, R. E., Quantum turbulence in a propagating superfluid vortex front, Phys. Rev. Lett., 2007, 99, 265301. CrossRef | |
| Landau, L. D. and Lifshitz, E. M., Fluid mechanics, 2nd edn., Pergamon Press, Oxford, 1987. | |
| Donnelly, R. J., private communication. | |
| Jäger, J., Schuderer, B. and Schoepe, W., Turbulent and laminar drag of superfluid helium on an oscillating microsphere, Phys. Rev. Lett., 1995, 74, 566-569. CrossRef | |
| Awschalom, D. D. and Schwarz, K. W., Observation of a remanent vorte-line density in superfluid helium, Phys. Rev. Lett., 1984, 52, 49-52. CrossRef | |
| Hänninen, R., Tsubota, M. and Vinen, W. F., Generation of turbulence by oscillating structures in superfluid helium at very low temperatures, Phys. Rev. B, 2007, 75, 064502. CrossRef | |
| Zhang, T. and Van Sciver, S. W., Large-scale turbulent flow around a cylinder in counterfow superfluid 4He (He(II)), Nature Phys., 2005, 1, 36-38. CrossRef | |
| Poole, D. R., Barenghi, C. F., Sergeev, Y. A. and Vinen, W. F., Motion of tracer particles in He II, Phys. Rev. B, 2005, 71, 064514. CrossRef | |
| Kivotides, D., Barenghi, C. F. and Sergeev, Y. A., Collision of a tracer particle and a quantized vortex in superfluid helium: Self-consistent calculations, Phys. Rev. B, 2007, 75, 212502. CrossRef | |
| Kivotides, D., Barenghi, C. F. and Sergeev, Y. A., Interactions between particles and quantized vortices in superfluid helium, Phys. Rev. B, 2008, 014527. | |
| Bewley, G. P., Lathrop, D. P. and Sreenivasan, K. R., Visualization of quantized vortices, Nature, 2006, 441, 588. CrossRef | |
| Paelotti, M. S., Firrito, R. B., Sreenivasan, K. R. and Lathrop, D. P., Visualization of superfluid helium flow, J. Phys. Soc. Jpn., 2008, 77, 111007. CrossRef | |
| Kobayashi, M. and Tsubota, M., Quantum turbulence in a trapped Bose-Einstein condensate, Phys. Rev. A, 2007, 76, 045603. CrossRef | |
| Goto, S., Ishii, N., Kida, S. and Nishioka, M., Turbulence generator using a precessing sphere, Phys. Fluids, 2007, 19, 061705. CrossRef | |
| Kobayashi, M. and Tsubota, M., Quantum turbulence in a trapped Bose-Einstein condensate under combined rotations around three axes, J. Low Temp. Phys., 2008, 150, (2008), 587-592. CrossRef | |
| Stenger, J., Inouye, S., Chikkatur, A. P., Stamper-Kurn, D. M., Pritchard, D. E. and Ketterle, W., Bragg spectroscopy of a Bose-Einstein condensate, Phys. Rev. Lett., 1999, 82, 4569-4573. CrossRef | |
| Kasamatsu, K., Tsubota, M. and Ueda, M., Vortices in multicomponent Bose-Einstein condensates, Int. J. Mod. Phys. B, 2005, 19, 1835-1904. CrossRef | |
| Henn, E. A. L., Seman, J. A., Roati, G., Magalhaes, K. M. F. and Bagnato, V. S., Emergence of turbulence in an oscillating Bose-Einstein condensate, Phys. Rev. Lett., 2009, 103, 045301. CrossRef |
Quantum Turbulence
Makoto TsubotaRelated information
1 Department of Physics, Osaka City University, Japan