Equilibrium vortex formation in ultrarapidly rotating two-component Bose-Einstein condensates

Equilibrium vortex formation in rotating binary Bose gases with a rotating frequency higher than the harmonic trapping frequency is investigated theoretically. We consider the system being evaporatively cooled to form condensates and a combined numerical scheme is applied to ensure the binary system being in an authentic equilibrium state. To keep the system stable against the large centrifugal force of ultrafast rotation, a quartic trapping potential is added to the existing harmonic part. Using the Thomas-Fermi approximation, a critical rotating frequency \Omega_c is derived, which characterizes the structure with or without a central density hole. Vortex structures are studied in detail with rotation frequency both above and below ?\Omega_c and with respect to the miscible, symmetrically separated, and asymmetrically separated phases in their nonrotating ground-state counterparts.Comment: 7 pages, 7 figure

Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation

Transcritical flow of a stratified fluid past a broad localised topographic obstacle is studied analytically in the framework of the forced extended Korteweg--de Vries (eKdV), or Gardner, equation. We consider both possible signs for the cubic nonlinear term in the Gardner equation corresponding to different fluid density stratification profiles. We identify the range of the input parameters: the oncoming flow speed (the Froude number) and the topographic amplitude, for which the obstacle supports a stationary localised hydraulic transition from the subcritical flow upstream to the supercritical flow downstream. Such a localised transcritical flow is resolved back into the equilibrium flow state away from the obstacle with the aid of unsteady coherent nonlinear wave structures propagating upstream and downstream. Along with the regular, cnoidal undular bores occurring in the analogous problem for the single-layer flow modeled by the forced KdV equation, the transcritical internal wave flows support a diverse family of upstream and downstream wave structures, including solibores, rarefaction waves, reversed and trigonometric undular bores, which we describe using the recent development of the nonlinear modulation theory for the (unforced) Gardner equation. The predictions of the developed analytic construction are confirmed by direct numerical simulations of the forced Gardner equation for a broad range of input parameters.Comment: 34 pages, 24 figure

Bending-wave Instability of a Vortex Ring in a Trapped Bose-Einstein Condensate

Based on a velocity formula derived by matched asymptotic expansion, we investigate the dynamics of a circular vortex ring in an axisymmetric Bose-Einstein condensate in the Thomas-Fermi limit. The trajectory for an axisymmetrically placed and oriented vortex ring is entirely determined, revealing that the vortex ring generally precesses in condensate. The linear instability due to bending waves is investigated both numerically and analytically. General stability boundaries for various perturbed wavenumbers are computed. In particular, the excitation spectrum and the absolutely stable region for the static ring are analytically determined.Comment: 4 pages, 4 figure

Stationary wave patterns generated by an impurity moving with supersonic velocity through a Bose-Einstein condensate

Formation of stationary 3D wave patterns generated by a small point-like impurity moving through a Bose-Einstein condensate with supersonic velocity is studied. Asymptotic formulae for a stationary far-field density distribution are obtained. Comparison with three-dimensional numerical simulations demonstrates that these formulae are accurate enough already at distances from the obstacle equal to a few wavelengths.Comment: 7 pages, 3 figure

Spontaneous Crystallization of Skyrmions and Fractional Vortices in the Fast-rotating and Rapidly-quenched Spin-1 Bose-Einstein Condensates

We investigate the spontaneous generation of crystallized topological defects via the combining effects of fast rotation and rapid thermal quench on the spin-1 Bose-Einstein condensates. By solving the stochastic projected Gross-Pitaevskii equation, we show that, when the system reaches equilibrium, a hexagonal lattice of skyrmions, and a square lattice of half-quantized vortices can be formed in a ferromagnetic and antiferromagnetic spinor BEC, respetively, which can be imaged by using the polarization-dependent phase-contrast method

Wearable, Multimodal, Biosignal Acquisition System for Potential Critical and Emergency Applications

For emergency or intensive-care units (ICUs), patients with unclear consciousness or unstable hemodynamics often require aggressive monitoring by multiple monitors. Complicated pipelines or lines increase the burden on patients and inconvenience for medical personnel. Currently, many commercial devices provide related functionalities. However, most devices measure only one biological signal, which can increase the budget for users and cause difficulty in remote integration. In this study, we develop a wearable device that integrates electrocardiography (ECG), electroencephalography (EEG), and blood oxygen machines for medical applications with the hope that it can be applied in the future. We develop an integrated multiple-biosignal recording system based on a modular design. The developed system monitors and records EEG, ECG, and peripheral oxygen saturation (SpO2) signals for health purposes simultaneously in a single setting. We use a logic level converter to connect the developed EEG module (BR8), ECG module, and SpO2 module to a microcontroller (Arduino). The modular data are then smoothly encoded and decoded through consistent overhead byte stuffing (COBS). This developed system has passed simulation tests and exhibited proper functioning of all modules and subsystems. In the future, the functionalities of the proposed system can be expanded with additional modules to support various emergency or ICU applications

Derivation of the Cubic Non-linear Schr\"odinger Equation from Quantum Dynamics of Many-Body Systems

We prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the cubic non-linear Schr\"odinger equation in a suitable scaling limit. The result is extended to $k$-particle density matrices for all positive integer $k$.Comment: 72 pages, 17 figures. Final versio

Selective interlayer ferromagnetic coupling between the Cu spins in YBa2_2 Cu3_3 O7−x_{7-x} grown on top of La0.7_{0.7} Ca0.3_{0.3} MnO3_3

Studies to date on ferromagnet/d-wave superconductor heterostructures focus mainly on the effects at or near the interfaces while the response of bulk properties to heterostructuring is overlooked. Here we use resonant soft x-ray scattering spectroscopy to reveal a novel c-axis ferromagnetic coupling between the in-plane Cu spins in YBa$_2$ Cu$_3$ O$_{7-x}$ (YBCO) superconductor when it is grown on top of ferromagnetic La$_{0.7}$ Ca$_{0.3}$ MnO$_3$ (LCMO) manganite layer. This coupling, present in both normal and superconducting states of YBCO, is sensitive to the interfacial termination such that it is only observed in bilayers with MnO_2but not with La$_{0.7}$ Ca$_{0.3}$ interfacial termination. Such contrasting behaviors, we propose, are due to distinct energetic of CuO chain and CuO$_2$ plane at the La$_{0.7}$ Ca$_{0.3}$ and MnO$_2$ terminated interfaces respectively, therefore influencing the transfer of spin-polarized electrons from manganite to cuprate differently. Our findings suggest that the superconducting/ferromagnetic bilayers with proper interfacial engineering can be good candidates for searching the theorized Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state in cuprates and studying the competing quantum orders in highly correlated electron systems.Comment: Please note the change of the title. Text might be slightly different from the published versio

Lower Bound on the Blow-up Rate of the Axisymmetric Navier-Stokes Equations

Consider axisymmetric strong solutions of the incompressible Navier-Stokes equations in R 3 with non-trivial swirl. Such solutions are not known to be globally defined, but it is shown in [11, 1] that they could only blow up on the axis of symmetry. Let z denote the axis of symmetry and r measure the distance to the z-axis. Suppose the solution satisfies the pointwise scale invariant bound |v(x, t)| ≤ C∗(r 2 − t) −1/2 for −T0 ≤ t < 0 and 0 < C∗ < ∞ allowed to be large, we then prove that v is regular at time zero.Mathematic