Article
Mathematics
Shunlin Shen
Summary: This study rigorously derives the 2D periodic focusing cubic NLS as the mean-field limit of the 3D focusing quantum many-body dynamics for a dilute Bose gas, and highlights the need for additional restrictions on system parameters to observe NLS dynamics in experiments.
JOURNAL OF FUNCTIONAL ANALYSIS
(2021)
Article
Engineering, Mechanical
Li Li, Fajun Yu
Summary: The PT-symmetric Gross-Pitaevskii equation and its generalized form, GGP(n,n), are introduced in this study. A kind of flat-top soliton solution is derived for the nonautonomous GGP(n,n) equation with Gaussian-harmonic-radial PT-symmetric potential. Novel flat-top bright solitons are found, and their interaction dynamics are investigated numerically.
NONLINEAR DYNAMICS
(2022)
Article
Optics
N. Korneev, V. Vysloukh
Summary: The study shows that the Gross-Pitaevskii equation with a parabolic potential has solutions in the form of localized wave packets, which exhibit self-similarity and undergo periodic spatial oscillations. These proposed solutions combine the properties of coherent states in quantum optics and solitons in the nonlinear Schrodinger equation, and are expressed as spatially shifted and phase-modulated solutions of a nonlinear second-order ordinary differential equation.
Article
Multidisciplinary Sciences
Tamil Arasan Bakthavatchalam, Suriyadeepan Ramamoorthy, Malaikannan Sankarasubbu, Radha Ramaswamy, Vijayalakshmi Sethuraman
Summary: Machine learning methods can efficiently model physical phenomena using scattered, noisy observations, with Gaussian Processes (GPs) showing promise in accurately reproducing ground state wave functions of BECs. The method's versatility and speed in generating results make it a viable alternative to existing numerical simulation techniques, requiring only a fraction of data points for similar levels of accuracy.
SCIENTIFIC REPORTS
(2021)
Article
Physics, Multidisciplinary
Alice Roitberg, Renzo L. Ricca
Summary: The study reveals a hydrodynamic interpretation of the Gross-Pitaevskii equation for Bose-Einstein condensates in a general Riemannian metric, highlighting a new term in the momentum equation related to local curvature and density distribution profile. Additionally, a new Einstein's field equation is determined under conditions of negative curvature, and a relativistic form of GPE is considered to show connections with analogue gravity models, suggesting further investigation into black hole dynamics in cosmology.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2021)
Article
Physics, Multidisciplinary
Shi-min Liu, Da-jun Zhang
Summary: In this paper, integrable Gross-Pitaevskii equations and integrable vector Gross-Pitaevskii systems are presented, and their relationship with nonlinear Schrodinger equations is discussed. Gauge transformations between different equations are derived, and a series of conservation laws are obtained. The solutions and dynamics are analyzed and localized-like waves are observed.
COMMUNICATIONS IN THEORETICAL PHYSICS
(2022)
Article
Physics, Multidisciplinary
Li Li, Fajun Yu
Summary: Nonautonomous bright-dark solitons and nonautonomous controllable behaviors are derived in the conformable space-time fractional Gross-Pitaevskii equation with external potentials. The relations between the space-time FGP equation and the fractional nonlinear Schrödinger equation are considered and the properties of the equation with group velocity dispersion and spatiotemporal dispersion are analyzed. Constraint conditions for valid soliton solutions are given. The effect of α and β in NBDSs of the space-time FGP equation is investigated, and different propagation dynamics are generated based on different values of α and β. Novel bright and 'h'-shape dark soliton solutions, as well as interactions of nonautonomous bright-dark solitons, are studied. The reported results provide insights into models of electrical and optical fields.
COMMUNICATIONS IN THEORETICAL PHYSICS
(2023)
Article
Physics, Multidisciplinary
Bin Liu, Yi Xi Chen, Ao Wei Yang, Xiao Yan Cai, Yan Liu, Zhi Huan Luo, Xi Zhou Qin, Xun Da Jiang, Yong Yao Li, Boris A. Malomed
Summary: This study investigates the stability and characteristics of two-dimensional vortex ring-shaped quantum droplets (QDs) formed by binary Bose-Einstein condensates. The study proposes an experimentally relevant method for the creation of vortical QDs and identifies the trapping capacity of the circular troughs for vortex rings with different winding numbers (WNs). The results also show the construction of stable compound states combining narrow rings and azimuthal solitons.
NEW JOURNAL OF PHYSICS
(2022)
Article
Physics, Multidisciplinary
N. Korneev, E. Francisco, V. A. Vysloukh
Summary: The study shows that coherent-solitonic states of the Gross-Pitaevskii equation with parabolic potential are linearly stable under certain conditions, but unstable perturbations may develop. Stabilization can be achieved by increasing the state intensity.
Article
Mathematics, Applied
Emmanuel Kengne, Boris A. Malomed, WuMing Liu
Summary: The study examines the cubic Gross-Pitaevskii equation governing the dynamics of BoseEinstein condensates with time-dependent coefficients and the generation of chirped rogue wave states. The results demonstrate that temporal modulation of the s-wave scattering length and strength of the inverted parabolic potential can manipulate the evolution of rogue matter waves in BEC.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Physics, Multidisciplinary
Sh N. Mardonov, E. Ya Sherman
Summary: The study investigates the coherent coupled motion of a polaron and a one-dimensional Bose-Einstein condensate in a harmonic potential. The dynamics of the system are strongly nonlinear and heavily influenced by the sign of self-interaction within the condensate and the interaction between the polaron-forming particle and the condensate. The research focuses on the interdependence of the condensate shape, center of mass position, and polaron coordinate during coupled nonlinear polaron-condensate oscillations and transmission/reflection episodes.
Article
Optics
Javed Akram
Summary: The study explores the quantum dynamics of two impurities in a trapped quasi-one-dimensional Bose-Einstein condensate, revealing the impact of impurity-BEC and impurity-impurity interaction strengths on impurities within the condensate. Strong interaction strengths suppress the back-and-forth motion of impurities. The findings suggest that quench dynamics can be a valuable tool for studying impurity-BEC and impurity-impurity interactions.
APPLIED PHYSICS B-LASERS AND OPTICS
(2021)
Article
Optics
C. Madronero, R. Paredes
Summary: A dynamic stability has been observed in a weakly interacting Bose gas of ultracold 23Na atoms in a moire lattice, similar to the phenomena seen in correlated electrons. The study demonstrates this stability by tracking the time evolution of two magnetic domains in the moire lattice. Square moire lattices exhibit dynamic stability for angles larger than a certain value, while hexagonal lattices show stability starting from a specific angle.
Article
Mathematics, Applied
Piotr Bizon, Filip Ficek, Dmitry E. Pelinovsky, Szymon Sobieszek
Summary: This study revisited the energy super-critical Gross-Pitaevskii equation with a harmonic potential, specifically in the case of cubic focusing nonlinearity and dimension d > 5. By developing the shooting method and dealing with a one-parameter family of classical solutions, the existence of ground state and the nature of solution curve were proven for different dimensions. Compared to existing literature, rigorous asymptotics were derived using functional-analytic methods to construct three families of solutions.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2021)
Article
Mathematics, Applied
Qiqi Tran, Jinjie Liu
Summary: In this paper, two modified ICN algorithms are proposed to achieve second order convergence rate by using different weight choices. The first approach uses geometrically averaged weights in two consecutive iterations, while the second approach uses arithmetically averaged weights for two consecutive time steps. The stability and second order accuracy of these methods are verified and demonstrated through numerical experiments.
NUMERICAL ALGORITHMS
(2023)
