We consider the motion of a matter-wave bright soliton under the influence of a cloud of thermal particles. In the ideal one-dimensional system, the scattering process of the quasiparticles with the soliton is reflectionless; however, the quasiparticles acquire a phase shift. In the realistic system of a Bose-Einstein condensate confined in a tight waveguide trap, the transverse degrees of freedom generate an extra nonlinearity in the system which gives rise to finite reflection and leads to dissipative motion of the soliton. We calculate the velocity and temperature-dependent frictional force and diffusion coefficient of a matter-wave bright soliton immersed in a thermal cloud.

The small-angle scattering curves of deterministic mass fractals are studied and analyzed in momentum space. In the fractal region, the curve I(q)q(D) is found to be log-periodic with good accuracy, and the period is equal to the scaling factor of the fractal. Here, D and I(q) are the fractal dimension and the scattering intensity, respectively. The number of periods of this curve coincides with the number of fractal iterations. We show that the log-periodicity of I(q)q(D) in the momentum space is related to the log-periodicity of the quantity g(r)r(3-D) in the real space, where g(r) is the pair distribution function. The minima and maxima positions of the scattering intensity are estimated explicitly by relating them to the pair distance distribution in real space. It is shown that the minima and maxima are damped with increasing polydispersity of the fractal sets; however, they remain quite pronounced even at sufficiently large values of polydispersity. A generalized self-similar Vicsek fractal with controllable fractal dimension is introduced, and its scattering properties are studied to illustrate the above findings. In contrast with the usual methods, the present analysis allows us to obtain not only the fractal dimension and the edges of the fractal region, but also the fractal iteration number, the scaling factor, and the number of structural units from which the fractal is composed.

Correlation functions related to the dynamic density response of the one-dimensional Bose gas in the model of Lieb and Liniger are calculated. An exact Bose-Fermi mapping is used to work in a fermionic representation with a pseudopotential Hamiltonian. The Hartree-Fock and generalized random phase approximations are derived and the dynamic polarizability is calculated. The results are valid to first order in 1/γ where γ is Lieb-Liniger coupling parameter. Approximations for the dynamic and static structure factor at finite temperature are presented. The results preclude superfluidity at any finite temperature in the large-γ regime due to the Landau criterion. Due to the exact Bose-Fermi duality, the results apply for spinless fermions with weak p-wave interactions as well as for strongly interacting bosons.

The one-dimensional Bose gas is an unusual superfluid. In contrast to higher spatial dimensions, the existence of non-classical rotational inertia is not directly linked to the dissipationless motion of infinitesimal impurities. Recently, experimental tests with ultracold atoms have begun and quantitative predictions for the drag force experienced by moving obstacles have become available. This topical review discusses the drag force obtained from linear response theory in relation to Landau's criterion of superfluidity. Based upon improved analytical and numerical understanding of the dynamical structure factor, results for different obstacle potentials are obtained, including single impurities, optical lattices and random potentials generated from speckle patterns. The dynamical breakdown of superfluidity in random potentials is discussed in relation to Anderson localization and the predicted superfluid-insulator transition in these systems.Comment: 17 pages, 12 figures, mini-review prepared for the special issue of Frontiers of Physics "Recent Progresses on Quantum Dynamics of Ultracold Atoms and Future Quantum Technologies", edited by Profs. Lee, Ueda, and Drummon

While the 1D Bose gas appears to exhibit superfluid response under certain conditions, it fails the Landau criterion according to the elementary excitation spectrum calculated by Lieb. The apparent riddle is solved by calculating the dynamic structure factor of the Lieb-Liniger 1D Bose gas. A pseudopotential Hamiltonian in the fermionic representation is used to derive a Hartree-Fock operator, which turns out to be well-behaved and local. The Random-Phase approximation for the dynamic structure factor based on this derivation is calculated analytically and is expected to be valid at least up to first order in 1/γ, where γ is the dimensionless interaction strength of the model. The dynamic structure factor in this approximation clearly indicates a crossover behavior from the non-superfluid Tonks to the superfluid weakly-interacting regime, which should be observable by Bragg scattering in current experiments.The emergence of superfluidity at low temperatures is one of the most dramatic manifestations of quantum many-body physics in nature. Although the gas of interacting Bosons in 1D is described by the exactly solvable Lieb-Liniger (LL) model [1,2], the question of superfluidity is not readily answered from the exact solutions. The dimensionless interaction parameter γ = g B m/(h 2 n) [1] governs the crossover from the weakly-interacting quasicondensate for γ ≪ 1 to the strongly-interacting Tonks-Girardeau gas [3] at γ = ∞, where g B is the coupling constant of the 1D Bose gas [4], n is the line density, and m is the particle mass. The Landau criterion of superfluidity [5] predicts a critical velocity v c for the breakdown of dissipationless flow if no elementary excitations of momentum p are accessible with energy below pv c to dissipate its energy. The excitation spectrum of the LL model [2] contains umklapp excitations at finite momentum 2πn and energies which tend to zero in a large system predicting a critical velocity of zero by the Landau criterion for any value of γ [see the lower thin (blue) line in Fig. 1]. On the other hand, Luttinger-liquid theory and instanton techniques [6,7] predict superfluidity in the LL model for sufficiently small γ. A resolution of this apparent paradox lies in the probability of excitation by an infinitesimal external perturber which is given by the dynamic structure factor (DSF) S(q, ω), the Fourier transform of the time-dependent density-density correlation function.

We consider a fractal with a variable fractal dimension, which is a generalization of the well known triadic Cantor set. In contrast with the usual Cantor set, the fractal dimension is controlled using a scaling factor, and can vary from zero to one in one dimension and from zero to three in three dimensions. The intensity profile of small-angle scattering from the generalized Cantor fractal in three dimensions is calculated. The system is generated by a set of iterative rules, each iteration corresponding to a certain fractal generation. Small-angle scattering is considered from monodispersive sets, which are randomly oriented and placed. The scattering intensities represent minima and maxima superimposed on a power law decay, with the exponent equal to the fractal dimension of the scatterer, but the minima and maxima are damped with increasing polydispersity of the fractal sets. It is shown that for a finite generation of the fractal, the exponent changes at sufficiently large wave vectors from the fractal dimension to four, the value given by the usual Porod law. It is shown that the number of particles of which the fractal is composed can be estimated from the value of the boundary between the fractal and Porod regions. The radius of gyration of the fractal is calculated analytically.

By using a close similarity between multi-photon and tunneling population transfer schemes, we propose robust adiabatic methods for the transport of Bose-Einstein condensate (BEC) in doubleand triple-well traps. The calculations within the mean-field approximation (Gross-Pitaevskii equation) show that irreversible and complete transport takes place even in the presence of the nonlinear effects caused by interaction between BEC atoms. The transfer is driven by adiabatic timedependent monitoring the barriers and well depths. The proposed methods are universal and can be applied to a variety of systems and scenarios.

We discuss approximate formulas for the dynamic structure factor of the one-dimensional Bose gas in the Lieb-Liniger model that appear to be applicable over a wide range of the relevant parameters such as the interaction strength, frequency, and wavenumber. The suggested approximations are consistent with the exact results known in limiting cases. In particular, we encompass exact edge exponents as well as Luttinger liquid and perturbation theoretic results. We further discuss derived approximations for the static structure factor and the pair distribution function g(x). The approximate expressions show excellent agreement with numerical results based on the algebraic Bethe ansatz.