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This study investigates the formation and dynamics of solitons in Bose–Einstein condensates (BECs) within dark traps generated by two crossed Laguerre–Gaussian (LG) beams with varying azimuthal indices ℓ . As the index ℓ increases, the potential transitions from a harmonic trap when ℓ = 1 to a square-well potential for larger values of ℓ . This transition allows us to study a range of soliton dynamics under different confinement conditions while maintaining the same BEC volume. Through the derivation of the Gross-Pitaevskii equation (GPE) and under these specific conditions in both one-dimensional and two-dimensional configurations, we explore the dynamics of solitons across multiple scenarios. The study examines two primary methods for solitons generation: the temporal modulation of the scattering length and the implementation of an initial potential barrier that is subsequently removed. The results indicate that the trap shape plays a critical role in the generation and interaction dynamics of solitons. In harmonic traps, solitons exhibit a behavior different from those observed in anharmonic traps, where the dynamics is significantly influenced by the azimuthal index of the trap. The ability to control soliton dynamics in BECs holds significant promise for applications in quantum technologies, precision sensing, and the exploration of fundamental quantum phenomena. [ABSTRACT FROM AUTHOR]

The sun is a fundamental element of the natural environment, and kinetic equations are crucial mathematical models for determining how quickly the chemical composition of a star like the sun is changing. Taking motivation from these facts, we develop and solve a novel fractional kinetic equation containing Fermi–Dirac (FD) and Bose–Einstein (BE) functions. Several distributional properties of these functions and their proposed new generalizations are investigated in this article. In fact, it is proved that these functions belong to distribution space  D ′ while their Fourier transforms belong to  Z ′. Fourier and Laplace transforms of these functions are computed by using their distributional representation. Thanks to them, we can compute various new fractional calculus formulae and a new relation involving the Fox–Wright function. Some fractional kinetic equations containing the FD and BE functions are also formulated and solved. [ABSTRACT FROM AUTHOR]

In this work, we consider the numerical computation of ground states and dynamics of single-component Bose–Einstein condensates (BECs). The corresponding models are spatially discretized with a multiscale finite element approach known as Localized Orthogonal Decomposition (LOD). Despite the outstanding approximation properties of such a discretization in the context of BECs, taking full advantage of it without creating severe computational bottlenecks can be tricky. In this paper, we therefore present two fully-discrete numerical approaches that are formulated in such a way that they take special account of the structure of the LOD spaces. One approach is devoted to the computation of ground states and another one for the computation of dynamics. A central focus of this paper is also the discussion of implementation aspects that are very important for the practical realization of the methods. In particular, we discuss the use of suitable data structures that keep the memory costs economical. The paper concludes with various numerical experiments in 1d, 2d and 3d that investigate convergence rates and approximation properties of the methods and which demonstrate their performance and computational efficiency, also in comparison to spectral and standard finite element approaches. [ABSTRACT FROM AUTHOR]

We propose boson sampling from a system of coupled photons and Bose–Einstein condensed atoms placed inside a multi-mode cavity as a simulation process testing the quantum advantage of quantum systems over classical computers. Consider a two-level atomic transition far-detuned from photon frequency. An atom–photon scattering and interatomic collisions provide interactions that create quasiparticles and excite atoms and photons into squeezed entangled states, orthogonal to the atomic condensate and classical field driving the two-level transition, respectively. We find a joint probability distribution of atom and photon numbers within a quasi-equilibrium model via a hafnian of an extended covariance matrix. It shows a sampling statistics that is ♯P-hard for computing, even if only photon numbers are sampled. Merging cavity-QED and quantum-gas technologies into a hybrid boson sampling setup has the potential to overcome the limitations of separate, photon or atom, sampling schemes and reveal quantum advantage. [ABSTRACT FROM AUTHOR]

The article "PRAYER IN THE MONASTIC COMMUNITY OF BOSE" highlights the importance of prayer in the ecumenical community of Bose, where the word of God is sought to be placed at the center of prayer. It emphasizes the centrality of the Bible in the composition of prayers and the Eucharistic celebration as a call to the visible unity of Christians. Despite the division among the Churches, the Bose community seeks to live out shared faith through responsible Eucharistic practice. [Extracted from the article]

In this paper, we consider an energy-conserving continuous Galerkin discretization of the Gross–Pitaevskii equation with a magnetic trapping potential and a stirring potential for angular momentum rotation. The discretization is based on finite elements in space and time and allows for arbitrary polynomial orders. It was first analyzed by O. Karakashian and C. Makridakis (SIAM J. Numer. Anal. , 36(6) ,1779–1807, 1999) in the absence of potential terms and corresponding a priori error estimates were derived in |$2D$|⁠. In this work we revisit the approach in the generalized setting of the Gross–Pitaevskii equation with rotation and we prove uniform |$L^{\infty }$| -bounds for the corresponding numerical approximations in |$2D$| and |$3D$| without coupling conditions between the spatial mesh size and the time step size. With this result at hand, we are particularly able to extend the previous error estimates to the |$3D$| setting while avoiding artificial CFL conditions. [ABSTRACT FROM AUTHOR]

This research article investigates the dynamic characteristics of solitary waves within a medium exhibiting weak nonlinearity in dual-mode. Firstly, the three models are converted to dual-mode. The primary focus is to investigate the behavior of solitary waves in a system described by a fourth-order nonlinear Schrödinger (NLS) equation, which incorporates Kerr nonlinearity, weak nonlocality, parabolic law nonlinearity and diffraction. By employing ansatz methods, the study successfully derives various localized waveforms, including bright, dark and singular solitons, based on the governing model. The examination extends to investigating the influence of nonlocality and power coefficients on dynamics of bright, dark and singular solitons. The findings presented in this article represent a crucial advancement in understanding the generation of solitary waves in nonlinear media. As the examined model finds application in various fields such as plasma physics, Bose-Einstein condensates and others, these findings not only enhance our theoretical understanding but also pave the way for potential practical applications and the advancement of innovative technologies. [ABSTRACT FROM AUTHOR]

Objective: Ni-Ti memory alloys are unusual materials for hard-tissue replacement because of their unique superelasticity, good biocompatibility, high strength, low specific gravity, low magnetism, wear resistance, corrosion resistance and fatigue resistance. The current study aims to evaluate its mechanical properties and provide biomechanical basis for the clinical application of the prosthesis. Methods: Ten adult metacarpophalangeal joint specimens were randomly divided into a prosthesis group (n = 5, underwent metacarpophalangeal joint prosthesis) and a control group (n = 5, underwent sham operation). Firstly, the axial compression strength was tested with BOSE material testing machine to evaluate its biomechanical strength. Secondly, these specimens were tested for strain changes using BOSE material testing machine and GOM non-contact optical strain measurement system to evaluate the stress changes. Thirdly, fatigue test was performed between groups. Lastly, the mechanical wear of the metacarpophalangeal joint prosthesis was tested with ETK5510 material testing machine to study its mechanical properties. Results: Axial compression stiffness in the prosthesis group was greater than that in the control group in terms of 30 ° and 60 ° flexion positions (P < 0.05). There was no statistically significant difference between two groups with regards to axial compression stiffness and stress change test (P > 0.05). In the fatigue wear test, the mean mass loss in the prosthesis group's prosthesis was 17.2 mg and 17.619 mm3, respectively. The mean volume wear rate was 0.12%. There was no statistically significant difference in the maximum pull-out force of the metacarpal, phalangeal, and polymer polyethylene pads between the prosthesis group and the control group specimens. Conclusions: Ni-Ti memory alloy metacarpophalangeal joint prosthesis conforms to the biomechanical characteristics of metacarpophalangeal joints without implants, and the fatigue strength can fully meet the needs of metacarpophalangeal joint activities after joint replacement. [ABSTRACT FROM AUTHOR]

Based on the two-dimensional Gross–Pitaevskii equation model, we investigated the asymmetric vortex evolution of two-dimensional Bose–Einstein condensates in a harmonic potential trap with polar direction perturbation. This corresponds to the generation of an asymmetric vortex evolution mode under initial vortex light manipulation together with polar direction perturbation. Unlike most of the prior work on this topic that uses a pure numerical method for the system under study, we use an exact analytical method rather than numerical simulation to investigate the key features of the system evolution dynamics in this study. Based on the variational method, and for different system parameter settings including the strength of the harmonic oscillator potential and the nonlinear interaction, we derived two evolution modes, namely, the periodic evolution oscillation mode and the monotonic decay mode, and pictorially demonstrated the evolution patterns of the system. In addition, we investigated the scenario when the system is in the rotating state, which corresponds to the action of the quadratic centrifugal potential. Notably, we also identified the damping effects for the two modes with increasing angular velocity, whose upper limit value corresponds to the constant vortex pattern of the system. Our theoretical results can be used to guide the experimental investigation of asymmetric vortex evolution in two-dimensional Bose–Einstein condensates. [ABSTRACT FROM AUTHOR]

The vacuum expectation values of the field squared and energy-momentum tensor for a massless scalar field are investigated in the Milne universe with general number of spatial dimensions. The vacuum state depends on the choice of the mode functions in the canonical quantization procedure and we assume that the field is prepared in the conformal vacuum. As the first step an integral representation for the difference of the Wightman functions corresponding to the conformal and Minkowski vacua is derived. The mean field squared and energy-momentum tensor are obtained in the coincidence limit. It is shown that the Minkowski vacuum state is interpreted as a thermal one with respect to the conformal vacuum. The thermal factor is of the Bose-Einstein type in odd dimensional space and of the Fermi-Dirac type in even number of spatial dimensions. [ABSTRACT FROM AUTHOR]

This case is about the strategic decision of Bose Corporation (Bose) to close down its retail stores in North America, Europe, Japan, and Australia. Its retail stores at other locations around the world were to, however, remain open and continue operations. The case dwells upon Bose's relentless focus on research and development, which gave it a competitive edge over its rivals. The case details the travails of the retail industry and the onslaughts Bose faced from the e-commerce companies, which led to the closure of several of its retail businesses and a reduction in the number of its stores. Bose's online strategy is discussed in detail along with its use of social media and online marketing. While some analysts were in favor of the store shutdown, others were quite critical and opined that Bose was likely to return to its store format. The case ends with the question whether Bose's decision to shut down its stores was right and whether customers would purchase its products online without 'experiencing' the products in person. [ABSTRACT FROM AUTHOR]