Collapse and Bose-Einstein condensation in a trapped Bose-gas with negative scattering length

We find that the key features of the evolution and collapse of a trapped Bose condensate with negative scattering length are predetermined by the particle flux from the above-condensate cloud to the condensate and by 3-body recombination of Bose-condensed atoms. The collapse, starting once the number of Bose-condensed atoms reaches the critical value, ceases and turns to expansion when the density of the collapsing cloud becomes so high that the recombination losses dominate over attractive interparticle interaction. As a result, we obtain a sequence of collapses, each of them followed by dynamic oscillations of the condensate. In every collapse the 3-body recombination burns only a part of the condensate, and the number of Bose-condensed atoms always remains finite. However, it can comparatively slowly decrease after the collapse, due to the transfer of the condensate particles to the above-condensate cloud in the course of damping of the condensate oscillations.Comment: 11 pages, 3 figure

Dynamics of dark solitons in elongated Bose-Einstein condensates

We find two types of moving dark soliton textures in elongated Bose-Einstein condensates: non-stationary kinks and proper dark solitons. The former have a curved notch region and rapidly decay by emitting phonons and/or proper dark solitons. The proper moving solitons are characterized by a flat notch region and we obtain the diagram of their dynamical stability. At finite temperatures the dynamically stable solitons decay due to the thermodynamic instability. We develop a theory of their dissipative dynamics and explain experimental data.Comment: ~ 5 pages, 1 figur

Quantum fluctuations in coupled dark solitons in trapped Bose-Einstein condensates

We show that the quantum fluctuations associated with the Bogoliubov quasiparticle vacuum can be strongly concentrated inside dark solitons in a trapped Bose Einstein condensate. We identify a finite number of anomalous modes that are responsible for such quantum phenomena. The fluctuations in these anomalous modes correspond to the `zero-point' oscillations in coupled dark solitons.Comment: 4 pages, 3 figure

Lieb Mode in a Quasi One-Dimensional Bose-Einstein Condensate of Atoms

We calculate the dispersion relation associated with a solitary wave in a quasi-one-dimensional Bose-Einstein condensate of atoms confined in a harmonic, cylindrical trap in the limit of weak and strong interactions. In both cases, the dispersion relation is linear for long wavelength excitations and terminates at the point where the group velocity vanishes. We also calculate the dispersion relation of sound waves in both limits of weak and strong coupling.Comment: 4 pages, 2 ps figures, RevTe

Vortex Rings and Lieb Modes in a Cylindrical Bose-Einstein Condensate

We present a calculation of a solitary wave propagating along a cylindrical Bose-Einstein trap, which is found to be a hybrid of a one-dimensional (1D) soliton and a three-dimensional (3D) vortex ring. The calculated energy-momentum dispersion exhibits characteristics similar to those of a mode proposed sometime ago by Lieb within a 1D model, as well as some rotonlike features.Comment: 4 pages, 4 figure

Dissipative dynamics of vortex arrays in anisotropic traps

We discuss the dissipative dynamics of vortex arrays in trapped Bose-condensed gases and analyze the lifetime of the vortices as a function of trap anisotropy and the temperature. In particular, we distinguish the two regimes of the dissipative dynamics, depending on the relative strength of the mutual friction between the vortices and the thermal component, and the friction of the thermal particles on the trap anisotropy. We study the effects of heating of the thermal cloud by the escaping vortices on the dynamics of the system.Comment: RevTeX, 8 pages, 3 eps figure

Lead–lag relationships between global mean temperature and the atmospheric CO<inf>2</inf> content in dependence of the type and time scale of the forcing

© 2016 Elsevier B.V.By employing an Earth system model of intermediate complexity (EMIC) developed at the A.M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences (IAP RAS CM), mutual lags between global mean surface air temperature, T and the atmospheric CO2 content, q, in dependence of the type and time scale of the external forcing are explored. In the simulation, which follows the protocol of the Coupled Models Intercomparison Project, phase 5, T leads q for volcanically-induced climate variations. In contrast, T lags behind q for changes caused by anthropogenic CO2 emissions into the atmosphere. In additional idealized numerical experiments, driven by periodic external emissions of carbon dioxide into the atmosphere, T always lags behind q as expected. In contrast, if the model is driven by the periodic non-greenhouse radiative forcing, T leads q for the external forcing time scale ≤4 ×102 yr, while q leads T at longer scales. The latter is an example that lagged correlations do not necessarily represent causal relationships in a system. This apparently counter-intuitive result, however, is a direct consequence of i) temperature sensitivity of the soil carbon stock (which decreases if climate is warmed and increases if climate is cooled), ii) conservation of total mass of carbon in the system in the absence of external carbon emissions, iii) increased importance of the oceanic branch of the carbon cycle at longer time scales. The results obtained with an EMIC are further interpreted with a conceptual Earth system model consisting of an energy balance climate model and a globally averaged carbon cycle model. The obtained results have implications to the empirical studies attempting to understand the origins of the contemporary climate change by applying lead–lag relationships to empirical data