Bose—Einstein condensates with tunable spin—orbit coupling in the two-dimensional harmonic potential: The ground-state phases, stability phase diagram and collapse dynamics

Jiao, Chen; Liang, Jun-Cheng; Yu, Z. X.; Chen, Yan; Zhang, Aixia; Xue, Ju-Kui

doi:10.1007/s11467-022-1180-3

Cited by 3 publications

(1 citation statement)

References 54 publications

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“…There are interesting applications of this method in multiagent research such as Chen et al [52], Lasry and Lions [53]. The variational method [54,55] is a solution similar to that used in quantum mechanics for approximating the desired energy state by selecting wave functions whose parameters minimise the expected value of the energy. The neural network quantum states [56] approximate the solution using machine learning to minimise the variational energy.…”

Section: Related Workmentioning

confidence: 99%

Estimating the Expected Time to Enter and Leave a Common Target Area in Robotic Swarms

Passos

Marcolino

2023

Preprint

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Coordination algorithms are required to minimise congestion when every robot in a robotic swarm has a common target area to visit. Some of these algorithms use artificial potential fields to enable path planning to become distributed and local. An efficiency measure for comparing them is the time to complete a task in relation to the number of individuals in the swarm. In order to compare distinct solutions as the swarm grows, experiments with different numbers of robots must be simulated to form a plot of the function of the task completion time versus the number of robots or other parameters. Nevertheless, plotting it for many robots through simulation is time-consuming. Additionally, the inference of a global swarm behaviour as the task completion time from the local individual robot motion controller based on potential fields and other dynamical variables is intractable and requires experimental analysis. Based on that, we present equations for estimating the expected task completion time of state-of-the-art algorithms, robots using only attractive and repulsive force fields and mixed teams for the common target area problem in robotic swarms with not only the number of robots as input but also environment- and algorithm-related global variables, such as the size of the common target area and the working area, average speed and average distance between the robots. This paper is a fundamental first step to start a discussion on how better approximations can be achieved and which mathematical theories about local-to-global analysis are better suited to this problem.

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Section: Related Workmentioning

confidence: 99%

Estimating the Expected Time to Enter and Leave a Common Target Area in Robotic Swarms

Passos

Marcolino

2023

Preprint

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Interplay between spin-orbit couplings and residual interatomic interactions in the modulational instability of two-component Bose-Einstein condensates

et al. 2023

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Soliton molecules in coupled dipolar Bose–Einstein condensates with spin-orbit coupling

et al. 2023

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Recent research works on ultra cold quantum gases demonstrated that dipolar Bose–Einstein condensates (BECs) exhibit rich spatiotemporal dynamic where both local and nonlocal interactions are considered. We explore theoretically the possibility of controlling the formation and dynamics of soliton molecules in binary dipolar condensates with spin-orbit coupling (SOC). We exploit the variational technique to derive the new equations of motion for the widths and amplitudes, the effective potential and the oscillation frequency of the molecules. Our study confirms the existence of stable localized bound states in an optical potential. We find that the integrity of the molecules is influenced by the physical parameters, notably the local and nonlocal interactions with the SOC. These parameters are carefully chosen by the Vakhitov–Kolokolov (VK) criterion to ensure the stability of the molecules. We present the results of numerical experiments and confirm the analytical predictions. Moreover, we show the soliton–soliton interaction in each molecule when the local interactions are strong.

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Bose—Einstein condensates with tunable spin—orbit coupling in the two-dimensional harmonic potential: The ground-state phases, stability phase diagram and collapse dynamics

Cited by 3 publications

References 54 publications

Estimating the Expected Time to Enter and Leave a Common Target Area in Robotic Swarms

Estimating the Expected Time to Enter and Leave a Common Target Area in Robotic Swarms

Interplay between spin-orbit couplings and residual interatomic interactions in the modulational instability of two-component Bose-Einstein condensates

Soliton molecules in coupled dipolar Bose–Einstein condensates with spin-orbit coupling

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