We discuss recent important topics on hydrodynamics and turbulence in quantum fluids [1,2,3]. Quantum turbulence (QT) was discovered in superfluid 4He in the 1950s. QT is comprised of quantized vortices that are definite topological defects arising from the order parameter appearing in Bose-Einstein condensation. Quantum hydrodynamics and turbulence are still studied actively in superfluid 4He and 3He, but the realization of atomic Bose-Einstein condensation in 1995 has proposed another important stage for this issue. A general introduction to this issue and a brief review of the basic concepts are followed by some recent important developments. QT presents much more various worlds of turbulence than classical turbulence. 

In the latter half, we discuss three interesting topics of QT in atomic Bose-Einstein condensates (BECs). The first topic is turbulence of quantized vortices. Even in such a trapped system, quantized vortices can make turbulence with the Kolmogorov spectrum [4]. The second topic is spin turbulence (ST) in spinor BECs [5]. When the system is excited from the ground state, appears ST where the spin density vectors are spatially disordered (See the figure). ST is characterized by the novel -7/3 power law in the spectrum of the spin-dependent interaction energy. The direction of the spin density vector is spatially disordered but temporally frozen in ST, showing some analogy with spin glass state. When we introduce the order parameter of spin glass into ST, it grows with the appearance of the -7/3 power law. ST allows turbulence not only of spins but also of superfluids, the two kinds of turbulence sustaining each other through interaction. 

The third topic is wave turbulence of Bogoliubov excitations [6]. The study opens a way to observe a statistical law in atomic BECs for the first time. 

References

[1] Progress in Low Temperature Physics, ed. W. P. Halperin and M. Tsubota (Elsevier, Amsterdam, 2009) Vol.16.

[2] M. Tsubota, M. Kobayashi and H. Takeuchi, Phys. Rep. 522, 191 (2013).

[3] M. Tsubota, K. Kasamatsu and M. Kobayashi, in Novel Superfluids, ed. K. H. Bennemann and J. B. Ketterson (Oxford University Press, Oxford, 2013), Vol. 1, p.156. 

[4] M. Kobayashi and M. Tsubota, Phys. Rev. A76, 045603(2007). 

[5] K. Fujimoto, M. Tsubota. Phys. Rev. A85, 033642 (2012); Phys. Rev. A85, 053641 (2012); M. Tsubota, Y. Aoki, K. Fujimoto, Phys. Rev. A88, 061601(R) (2013); K. Fujimoto, M. Tsubota, Phys. Rev. A90, 013629(2014).

[6] K. Fujimoto and M. Tsubota, Phys. Rev.A 91, 053602 (2015).