Physics of quantized vortices in superfluid helium and atomic Bose-Einstein condensates

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We study theoretically and numerically physics of quantized vortices in superfluid helium and atomic Bose-Einstein condensates. The obtained results are the following.Superfluid helium1.We discovered an velocity-independent transition for superfluid turbulence in superfluid helium3 at ultra low temperatures.2.We found that the energy spectrum of superfluid turbulence obeys the Kolmogorov law which is the most important statistical law in classical turbulence.3.We discovered the Kelvin wave cascade process at very low temperatures that is supposed to be a dissipative mechanism.4.We found that a polarized vortex tangle appears in rotating superfluid turbulence.Atomic Bose-Einstein condensation1.We studied the structure of vortex lattices in rotating two-component Bose condensates.2.We studied three-dimensional dynamics of vortex lattice formation in rotating Bose condensates.3.We studied the mechanism of formation of multi domains in two-component Bose condensates.4.We studied collective excitations in two-component hose condensates.5.We studied spin texture in rotating two-component Bose condensates.6.We studied the ground state in rotating mixture of Bosons and Fermions.