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Motivated by a recent experiment [K. C. Wright et al., Phys. Rev. Lett. 110, 025302 (2013)], we investigate deterministic discontinuous jumps between quantized circulation states in a toroidally trapped Bose-Einstein condensate. These phase slips are induced by vortex excitations created by a rotating weak link. We analyze the influence of a localized condensate density depletion and atomic superflows, governed by the rotating barrier, on the energetic and dynamical stability of the vortices in the ring-shaped condensate. We simulate in a three-dimensional dissipative mean-field model the dynamics of the condensate using parameters similar to the experimental conditions. Moreover, we consider the dynamics of the stirred condensate far beyond the experimentally explored region and reveal surprising manifestations of complex vortex dynamics.

In a recent publication, J. Phys.: Condens. Matter 14 13777 (2002), Kuzovkov et al announced an analytical solution of the two-dimensional Anderson localisation problem via the calculation of a generalised Lyapunov exponent using signal theory. Surprisingly, for certain energies and small disorder strength they observed delocalised states. We study the transmission properties of the same model using well-known transfer matrix methods. Our results disagree with the findings obtained using signal theory. We point to the possible origin of this discrepancy and comment on the general strategy to use a generalised Lyapunov exponent for studying Anderson localisation.

Motivated by a recent experiment [S. Beattie, S. Moulder, R. J. Fletcher, and Z. Hadzibabic, PRL 110, 025301 (2013)] we study the superflow of atomic spinor Bose-Einstein condensates optically trapped in a ring-shaped geometry. Within a dissipative mean-field approach we simulate a twocomponent condensate in conditions adapted to the experiment. In qualitative agreement with the experimental findings, we observe persistent currents, if the spin-population imbalance is above some well-defined 'critical' value. The triply charged vortices decay in quantized steps. The vortex lines escape from the center of the ring through dynamically created regions in the condensate annulus with reduced density of one component filled by atoms of the other component. The vortices then leave the ring-shaped high density region of the condensate and finally decay into elementary excitations. Persistent currents or 'flows without friction' as a hallmark of superfluidity have been studied in liquid helium for several decades. Recently, persistent flow of atoms has been observed in Bose-Einstein condensates (BEC) trapped in a ring-like potential [1][2][3][4][5]. This enables fundamental studies of superfluidity and may lead to applications in high precision metrology and atomtronics. Of course, the question of the stability of the atomic persistent currents is of fundamental importance and, therefore, the subject of numerous investigations.Theoretical studies of persistent currents in atomic BEC are mostly limited to the simplified cases of one-dimensionality and very weak interactions. Onecomponent BECs in a one-dimensional (1D) ring potential were studied in Refs. [6] and [7]. Superfluidity on a 1D ring in the presence of impurities was investigated in Ref. [8]. Families of 2D solitary waves with and without singly-charged persistent flow are investigated in Ref. [9]. For two-component BECs in 1D or 2D traps, the stability of the persistent currents and their decay mechanisms were under investigation in Refs. [10][11][12][13][14][15][16]. Smyrnakis et al. [10] concluded that in a strictly one-dimensional ring persistent currents with circulation lager than one are stable only in single-component gases. This conclusion was challenged recently [17]. In Ref.[18] it was found on the basis of mean field calculations supported by exact diagonalization results, that persistent currents in 2D traps may be stable under specific conditions. Experimentally, this problem has been addressed very recently [5] for a toroidally trapped gas of 87 Rb atoms in two different spin states. However, previous theoretical investigations describe the stability of the persistent currents in spinor BEC only qualitatively, but do not elucidate the microscopic mechanism of the instabilities and its impact on the dynamics of the persistent currents.In the present work, we investigate the stability of the superflow within a two-dimensional dissipative meanfield theory. We find that phase-slips occur as the result of the simultaneous action of two factors: an azim...

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