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

Simulation of a stationary dark soliton in a trapped zero-temperature Bose-Einstein condensate

We discuss a computational mechanism for the generation of a stationary dark soliton, or black soliton, in a trapped Bose-Einstein condensate using the Gross-Pitaevskii (GP) equation for both attractive and repulsive interaction. It is demonstrated that the black soliton with a "notch" in the probability density with a zero at the minimum is a stationary eigenstate of the GP equation and can be efficiently generated numerically as a nonlinear continuation of the first vibrational excitation of the GP equation in both attractive and repulsive cases in one and three dimensions for pure harmonic as well as harmonic plus optical-lattice traps. We also demonstrate the stability of this scheme under different perturbing forces.Comment: 7 pages, 15 ps figures, Final version accepted in J Low Temp Phy

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

Dissipative dynamics of vortex arrays in trapped Bose-condensed gases: neutron stars physics on μ\muK scale

We develop a theory of dissipative dynamics of large vortex arrays in trapped Bose-condensed gases. We show that in a static trap the interaction of the vortex array with thermal excitations leads to a non-exponential decay of the vortex structure, and the characteristic lifetime depends on the initial density of vortices. Drawing an analogy with physics of pulsar glitches, we propose an experiment which employs the heating of the thermal cloud in the course of the decay of the vortex array as a tool for a non-destructive study of the vortex dynamics.Comment: 4 pages, revtex; revised versio

Dissipative dynamics of a kink state in a Bose-condensed gas

We develop a theory of dissipative dynamics of a kink state in a finite-temperature Bose-condensed gas. We find that due to the interaction with the thermal cloud the kink state accelerates towards the velocity of sound and continuously transforms to the ground-state condensate. We calculate the life-time of a kink state in a trapped gas and discuss possible experimental implications.Comment: 4 pages, RevTe

Greying of the Dark Soliton: Depletion in the Anomalous Mode of the Bogoliubov Theory

Quantum depletion from an atomic quasi one dimensional Bose-Einstein condensate with a dark soliton is studied in a framework of the Bogoliubov theory. Depletion is dominated by an anomalous mode localized in a notch of the condensate wave function. Depletion in the anomalous mode requires different treatment than depletion without anomalous modes. In particular, quantum depletion in the Bogoliubov vacuum of the anomalous mode is experimentally irrelevant. A dark soliton is initially prepared in a state with minimal depletion which is not a stationary state of the Bogoliubov theory. The notch fills up with incoherent atoms depleted from the condensate. For realistic parameters the filling time can be as short as 10 ms.Comment: 5 pages, version to appear in Phys.Rev.

Images of the Dark Soliton in a Depleted Condensate

The dark soliton created in a Bose-Einstein condensate becomes grey in course of time evolution because its notch fills up with depleted atoms. This is the result of quantum mechanical calculations which describes output of many experimental repetitions of creation of the stationary soliton, and its time evolution terminated by a destructive density measurement. However, such a description is not suitable to predict the outcome of a single realization of the experiment were two extreme scenarios and many combinations thereof are possible: one will see (1) a displaced dark soliton without any atoms in the notch, but with a randomly displaced position, or (2) a grey soliton with a fixed position, but a random number of atoms filling its notch. In either case the average over many realizations will reproduce the mentioned quantum mechanical result. In this paper we use N-particle wavefunctions, which follow from the number-conserving Bogoliubov theory, to settle this issue.Comment: 8 pages, 6 figures, references added in version accepted for publication in J. Phys.

Solitons in one-dimensional interacting Bose-Einstein system

A modified Gross-Pitaevskii approximation was introduced recently for bosons in dimension $d\le2$ by Kolomeisky {\it et al.} (Phys. Rev. Lett. {\bf 85} 1146 (2000)). We use the density functional approach with sixth-degree interaction energy term in the Bose field to reproduce the stationary-frame results of Kolomeisky {\it et al.} for a one-dimensional Bose-Einstein system with a repulsive interaction. We also find a soliton solution for an attractive interaction, which may be boosted to a finite velocity by a Galilean transformation. The stability of such a soliton is discussed analytically. We provide a general treatment of stationary solutions in one dimension which includes the above solutions as special cases. This treatment leads to a variety of stationary wave solutions for both attractive and repulsive interactions.Comment: Latex, 14 pages, No figur

On the stability of standing matter waves in a trap

We discuss excited Bose-condensed states and find the criterion of dynamical stability of a kink-wise state, i.e., a standing matter wave with one nodal plane perpendicular to the axis of a cylindrical trap. The dynamical stability requires a strong radial confinement corresponding to the radial frequency larger than the mean-field interparticle interaction. We address the question of thermodynamic instability related to the presence of excitations with negative energy.Comment: 4 pages, 3 figure