Article
Mathematics, Applied
Cheng-lin Wang, Jian Zhang
Summary: We studied the L-2-supercritical nonlinear Schrodinger equation (NLS) with partial confinement, which is a limit case of the cigar-shaped model in Bose-Einstein condensate (BEC). By constructing a cross constrained variational problem and establishing the invariant manifolds of the evolution flow, we obtained a sharp condition for global existence.
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
(2023)
Article
Optics
Boyao Li, Xingjie Wang, Yaoyao Liang, Jinghua Sun, Sufang Zhu, Xiaoyong Chen, Guiyao Zhou
Summary: This study reports the generation of vectorial solitons in a single cavity induced by dual-core fiber assisted ultrafast fiber lasers. It was found that four-component polarized rotation vector solitons (PRVS) are generated using the dispersive Fourier transformation technique. Furthermore, by controlling the soliton phase offset in dual-core fiber, the soliton rain state of multi pulse evolution can be obtained.
OPTICS AND LASER TECHNOLOGY
(2023)
Article
Mathematical & Computational Biology
Min Gong, Hui Jian, Meixia Cai
Summary: In this article, the global existence and stability issues of the nonlinear Schrödinger equation with partial confinement are considered. By establishing new cross-invariant manifolds and variational problems, a new sharp criterion for global existence is derived in different cases. The existence of orbitally stable standing waves is then obtained using the profile decomposition technique. This work extends and complements previous results.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Mathematics, Interdisciplinary Applications
Mikhail N. Smolyakov
Summary: In this paper, quantization of a weakly nonideal Bose gas at zero temperature is performed along the lines of the well-known Bogolyubov approach. By introducing nonoscillation modes and calculating nonlinear corrections, the analysis successfully recovers canonical commutation relations and solves the issue of nonconserved particle number at least in the case of free quasi-particles.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Optics
A. D. Garcia-Orozco, L. Madeira, M. A. Moreno-Armijos, A. R. Fritsch, P. E. S. Tavares, P. C. M. Castilho, A. Cidrim, G. Roati, V. S. Bagnato
Summary: We studied the emergence of universal scaling in the time-evolving momentum distribution of a harmonically trapped three-dimensional Bose-Einstein condensate, which was parametrically driven to a turbulent state. We found that the out-of-equilibrium dynamics post excitation can be described by a single function due to nearby nonthermal fixed points. The observed behavior connects the dynamics of a quantum turbulent state to several far-from-equilibrium phenomena.
Article
Multidisciplinary Sciences
Mengjie Wei, Wouter Verstraelen, Konstantinos Orfanakis, Arvydas Ruseckas, Timothy C. H. Liew, Ifor D. W. Samuel, Graham A. Turnbull, Hamid Ohadi
Summary: The authors demonstrate the on-the-fly reconfigurable optical trapping of organic polariton condensates, which are delocalized over a macroscopic distance from the excitation region. This study holds great potential for future research on polaritonic lattice physics.
NATURE COMMUNICATIONS
(2022)
Article
Mathematics, Applied
Argha Debnath, Ayan Khan, Boris Malomed
Summary: This study investigates the static and dynamical properties of one-dimensional quantum droplets under the influence of local potentials in the form of narrow wells and barriers. The dynamics of the droplets are described by the one-dimensional Gross-Pitaevskii equation, including meanfield and beyond-mean-field terms. Stable solutions for localized states pinned to the well are found, and approximations for the well and the collision of the droplet with the barrier are developed. Simulations analyze the collisions of droplets with the wells and barriers, identifying outcomes such as fission and rebound effects.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Materials Science, Multidisciplinary
Wen-Kai Bai, Jian-Chong Xing, Tao Yang, Wen-Li Yang, Wu-Ming Liu
Summary: In this study, the nonlinear dynamics of a three-dimensional Bose-Einstein condensate excited by a vortex ring phase imprinting were investigated. The amplitude and frequency of the center-of-mass oscillation of the condensate were found to be influenced by the initial radius of the vortex ring, nonlinear inter-atomic interactions, trap aspect ratio, and Kelvin wave perturbations. The parity of the wave number of Kelvin perturbations played a significant role in determining the mode of the center-of-mass oscillation of the condensate.
RESULTS IN PHYSICS
(2021)
Article
Engineering, Mechanical
Hong Cao
Summary: In this study, we investigate the effect of Rosen-Zener tunneling on Bose-Einstein condensates in a triple-well potential using mean-field treatment. We first calculate the tunneling dynamics exactly in the linear case and observe that all atoms are trapped in the initially populated well. However, the introduction of nonlinear interaction significantly changes the tunneling dynamics, breaking the symmetry and leading to the emergence of self-trapping solutions within a fixed interval.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Mikhail N. Smolyakov
Summary: The present paper continues the discussion of the canonical quantization of a weakly nonideal Bose gas at zero temperature within the framework of the Bogolyubov approach. In contrast to a previous paper on this subject, the general form of the two-body interaction potential is considered. It is shown that in this case, considering the first nonlinear correction also automatically leads to particle number conservation without any additional assumptions or modification of the resulting effective Hamiltonian.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Physics, Multidisciplinary
S. Baryshev, A. Zasedatelev, H. Sigurdsson, I Gnusov, J. D. Topfer, A. Askitopoulos, P. G. Lagoudakis
Summary: In this study, we conducted full polarization tomography on photon correlations in a spinor exciton-polariton condensate. Our measurements demonstrate the different forms of condensate pseudospin mean-field dynamics and their intrinsic relation to the condensate photon statistics.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Multidisciplinary
Hagai Edri, Boaz Raz, Gavriel Fleurov, Roee Ozeri, Nir Davidson
Summary: We studied the evolution of a Bose-Einstein condensate in a two-state superposition and successfully decoupled the system from strong magnetic noises. Our results show the impact of inter-state interactions on general superposition states and demonstrate squeezing of Gaussian noise using nonlinear spin dynamics. The scheme can be used for spin-squeezing beyond the standard quantum limit and observing polaron physics.
NEW JOURNAL OF PHYSICS
(2021)
Article
Multidisciplinary Sciences
Silvana Palacios Alvarez, Pau Gomez, Simon Coop, Roberto Zamora-Zamora, Chiara Mazzinghi, Morgan W. Mitchell
Summary: We present a magnetic sensor with extremely high energy resolution, applied in the detection of Rb-87 single-domain spinor Bose-Einstein condensates. By utilizing nondestructive Faraday rotation probing, we have achieved a low-frequency magnetic sensitivity of 72(8) fT, and measured the volume, spin coherence time, and readout noise of the condensate experimentally.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2022)
Article
Engineering, Mechanical
Emmanuel Kengne
Summary: In this study, we used the similarity transformation technique to build exact and approximate rogue wave (RW) solutions for a quasi-one-dimensional Gross-Pitaevskii equation. These solutions were applied to the study of matter rogue waves and superposed rogue waves in Bose-Einstein condensates (BECs), considering different forms of the interatomic interaction strength. The results show that the solution parameters can be used to control the formation and manipulation of first- and second-order RWs in BEC systems. Additionally, the effects of changing the parameters of the interatomic interaction strength were investigated, revealing the reduction of RWs to single solitons or multiplets. The control and free parameters in the RW solutions were found to influence the splitting of rogue wave components into multi-peak solutions. Furthermore, the linear superposition of different rogue wave solutions resulted in four types of coherent structures, which were analyzed in detail, along with the effects of solution parameters and intra-component strength.
NONLINEAR DYNAMICS
(2023)
Article
Optics
M. Miskeen Khan, H. Tercas, J. T. Mendonca, J. Wehr, C. Charalambous, M. Lewenstein, M. A. Garcia-March
Summary: The study investigates the quantum motion of an impurity atom in a Bose-Einstein condensate in arbitrary dimensions, showing superdiffusive behavior, dimension-dependent average energy, and non-Markovianity of particle motion. Trapped impurity atoms exhibit stronger position squeezing in lower dimensions.
Article
Mathematics, Applied
Guglielmo Feltrin, Maurizio Garrione
Summary: This article deals with a non-autonomous parameter-dependent second-order differential equation driven by a Minkowski-curvature operator. It proves the existence of strictly increasing heteroclinic solutions and homoclinic solutions with a unique change of monotonicity under suitable assumptions, and analyzes the asymptotic behavior of these solutions.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Mehraj Ahmad Lone, Idrees Fayaz Harry
Summary: In this paper, we study Lorentzian generalized Sasakian space forms admitting Ricci soliton, conformal gradient Ricci soliton, and Ricci Yamabe soliton. We also investigate the conditions for solitons to be steady, shrinking, and expanding. Additionally, we provide applications of Ricci Yamabe solitons.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Zhihao Lu
Summary: We present a unified method for deriving differential Harnack inequalities for positive solutions to semilinear parabolic equations, subject to an integral curvature condition, on compact manifolds and complete Riemannian manifolds. In addition to the case of scalar equations, we also establish an elliptic estimate for the heat flow under the same condition, which is a novel result for both harmonic map and heat equations.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Giuseppe Cosma Brusca
Summary: We investigate the asymptotic behavior of the minimal heterogeneous d-capacity of a small set in a fixed bounded open set Omega. We prove that this capacity is related to the parameter lambda and behaves as C |log epsilon|^(1-d), where C is a constant.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Stefan Schiffer
Summary: This note investigates the complex constant rank condition for differential operators and its implications for coercive differential inequalities. Depending on the order of the operators, such inequalities can be viewed as generalizations of either Korn's inequality or Sobolev's inequality.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Konstantinos T. Gkikas, Phuoc-Tai Nguyen
Summary: This article studies the boundary value problem with an inverse-square potential and measure data. By analyzing the Green kernel and Martin kernel and using appropriate capacities, necessary and sufficient conditions for the existence of a solution are established in different cases.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Giovanni Bellettini, Simone Carano, Riccardo Scala
Summary: This article computes the relaxed Cartesian area in the strict BV-convergence for a class of piecewise Lipschitz maps from the plane to the plane, where the jump is composed of multiple curves that are allowed to meet at a finite number of junction points. It is shown that the domain of this relaxed area is strictly contained within the domain of the classical L1-relaxed area.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Federico Cacciafesta, Anne-Sophie de Suzzoni, Long Meng, Jeremy Sok
Summary: In this paper, we establish the well-posedness of a perturbed Dirac equation with a moving potential W satisfying the Klein-Gordon equation. This serves as a toy model for atoms with relativistic corrections, where the wave function of electrons interacts with an electric field generated by a nucleus with a given charge density. A key contribution of this paper is the development of a new family of Strichartz estimates for time-dependent perturbations of the Dirac equation, which is of independent interest.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Jingwen Chen
Summary: In this article, the authors generalize their previous results to higher dimensions and prove the existence of eternal weak mean root 1 root-1 curvature flows connecting a Clifford hypersurface to the equatorial spheres.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Samuel Borza, Wilhelm Klingenberg
Summary: This article proves that the sub-Riemannian exponential map is not injective in any neighbourhood of certain critical points, and characterizes conjugate points in ideal sub-Riemannian manifolds in terms of the metric structure of the space.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Christina Sormani, Wenchuan Tian, Changliang Wang
Summary: This article presents a sequence of warped product manifolds that satisfy certain hypotheses and proves that this sequence converges in a weak sense to a limit space with nonnegative scalar curvature.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Gianni Dal Maso, Davide Donati
Summary: In this paper, we study the F-limits of sequences of quadratic functionals and bounded linear functionals on the Sobolev space, and show that their limits can always be expressed as the sum of a quadratic functional, a linear functional, and a non-positive constant. Furthermore, we prove that the coefficients of the quadratic and linear parts in the Gamma-limit are independent of Omega, and introduce an example to demonstrate that the previous results cannot be generalized to every bounded open set.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Laura Abatangelo, Corentin Lena, Paolo Musolino
Summary: The paper provides a full series expansion of a generalization of the u-capacity related to the Dirichlet-Laplacian in dimension three and higher. The results extend the previous findings on the planar case and are applied to study the asymptotic behavior of perturbed eigenvalues when Dirichlet conditions are imposed on a small regular subset of the domain.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Gustavo de Paula Ramos
Summary: This paper employs the photography method to estimate the number of solutions to a nonlinear elliptic problem on a Riemannian orbifold, based on the Lusternik-Schnirelmann category of its submanifold of points with the largest local group.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Tim Espin, Aram Karakhanyan
Summary: This article discusses smooth solutions of the Monge-Ampere equation on an annular domain with two smooth, closed, strictly convex hypersurfaces as boundaries, subject to mixed boundary conditions. It is demonstrated that global C2 estimates cannot be obtained in general unless additional restrictions are imposed on the principal curvatures of the inner boundary and the Neumann condition itself, as shown by an explicit counterexample. Under these conditions, a priori C2 estimates are proven and it is shown that the problem has a smooth solution.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
