Dynamic evolution of expanding Bose-Einstein condensates in the presence of a three-dimensional random optical speckle potential

We study the diffusion of an expanding Bose-Einstein condensate released from a harmonic trap in a three-dimensional speckle disorder potential. To this end, we use the first Born approximation and examine the density profiles at short and long times. Analytical results are presented in different regimes. The spatiotemporal evolution of the density profiles is examined. We find that at long times and for a fixed disorder strength, the profile of the atomic average density decreases in power law. The time evolution of the typical size of the condensate is explored numerically.

Boosting engine performance with Bose-Einstein condensation

At low-temperatures a gas of bosons will undergo a phase transition into a quantum state of matter known as a Bose-Einstein condensate (BEC), in which a large fraction of the particles will occupy the ground state simultaneously. Here we explore the performance of an endoreversible Otto cycle operating with a harmonically confined Bose gas as the working medium. We analyze the engine operation in three regimes, with the working medium in the BEC phase, in the gas phase, and driven across the BEC transition during each cycle. We find that the unique properties of the BEC phase allow for enhanced engine performance, including increased power output and higher efficiency at maximum power.

Charged stellar model with three layers

We establish new charged stellar models from the Einstein-Maxwell field equations for relativistic superdense objects outfitted with three layers. The core layer is described by a linear equation of state (EoS) describing quark matter, while the intermediate layer is described by a Bose-Einstein condensate EoS for Bose-Einstein condensate matter and the envelope layers satisfying a quadratic EoS for the neutron fluid. We have specified a new choice of the electric field and one of the metric potentials. It is interesting to note that the choice of electric field in this model can be set to vanish and we can regain earlier neutral models. Plots generated depict that the matter variables, gravitational potentials and other physical conditions are consistent with astrophysical studies. The interior layers and exterior boundary are also matched.

Exact Solutions for Solitary Waves in a Bose-Einstein Condensate under the Action of a Four-Color Optical Lattice

We address dynamics of Bose-Einstein condensates (BECs) loaded into a one-dimensional four-color optical lattice (FOL) potential with commensurate wavelengths and tunable intensities. This configuration lends system-specific symmetry properties. The analysis identifies specific multi-parameter forms of the FOL potential which admits exact solitary-wave solutions. This newly found class of potentials includes more particular species, such as frustrated double-well superlattices, and bichromatic and three-color lattices, which are subject to respective symmetry constraints. Our exact solutions provide options for controllable positioning of density maxima of the localized patterns, and tunable Anderson-like localization in the frustrated potential. A numerical analysis is performed to establish dynamical stability and structural stability of the obtained solutions, which makes them relevant for experimental realization. The newly found solutions offer applications to the design of schemes for quantum simulations and processing quantum information.

The Darboux Transformation and N-Soliton Solutions of Coupled Cubic-Quintic Nonlinear Schrödinger Equation on a Time-Space Scale

The coupled cubic-quintic nonlinear Schrödinger (CQNLS) equation is a universal mathematical model describing many physical situations, such as nonlinear optics and Bose–Einstein condensate. In this paper, in order to simplify the process of similar analysis with different forms of the coupled CQNLS equation, this dynamic system is extended to a time-space scale based on the Lax pair and zero curvature equation. Furthermore, Darboux transformation of the coupled CQNLS dynamic system on a time-space scale is constructed, and the N-soliton solution is obtained. These results effectively combine the theory of differential equations with difference equations and become a bridge connecting continuous and discrete analysis.