Band Structure of Bose-Einstein Condensates in a Cavity-Mediated Triple-Well System

We investigate the band structure and the dynamics of Bose-Einstein condensates in a triple-well trap,which are located in a high-finesse optical cavity.For the noninteracting atoms,the band structure of the eigenenergies are obtained using the numerical methods under the mean-field approximation.It is demonstrated that the energy band structure is strongly dependent on the value of reduced cavity detuning.Under some conditions,the atomic band structure develops loop structures and swallowtail structure,which mean the atom-cavity system exhibits bistability.We attribute the appearance of new states to the nonlinearity of the cavity-field-induced tilt.For the interacting atoms,the structure of the eigenenergy band appears more complicated for the interaction between atoms.

Pythagorean Fuzzy Einstein Aggregation Operators with Z-Numbers:Application in Complex Decision Aid Systems

The primary goal of this research is to determine the optimal agricultural field selection that would most effectively support manufacturing producers in manufacturing production while accounting for unpredictability and reliability in their decision-making.The PFS is known to address the levels of participation and non-participation.To begin,we introduce the novel concept of a PFZN,which is a hybrid structure of Pythagorean fuzzy sets and the ZN.The PFZN is graded in terms of membership and non-membership,as well as reliability,which provides a strong advice in real-world decision support concerns.The PFZN is a useful tool for dealing with uncertainty in decision-aid problems.The PFZN is a practical way for dealing with such uncertainties in decision-aid problems.The list of aggregation operators:PFZN Einstein weighted averaging and PFZN Einstein weighted geometric,is established under the novel Pythagorean fuzzy ZNs.It is a more precise mathematical instrument for dealing with precision and uncertainty.The core of this research is to develop a numerical algorithmto tackle the uncertainty in real-life problems using PFZNs.To show the applicability and effectiveness of the proposed algorithm,we illustrate the numerical case study related to determining the optimal agricultural field.The main purpose of this work is to describe the extended EDAS approach,then compare the proposed methodology with many other methodologies now in use,and then demonstrate how the suggested methodology may be applied to real-world problems.In addition,the final ranking results that were obtained by the devised techniques weremore efficient and dependable in comparison to the results provided by other methods presented in the literature.

Einstein’s Pseudo-Tensor in <i>n</i>Spatial Dimensions for Static Systems with Spherical Symmetry

It was noted earlier that the general relativity field equations for static systems with spherical symmetry can be put into a linear form when the source energy density equals radial stress. These linear equations lead to a delta function energymomentum tensor for a point mass source for the Schwarzschild field that has vanishing self-stress, and whose integral therefore transforms properly under a Lorentz transformation, as though the particle is in the flat space-time of special relativity (SR). These findings were later extended to n spatial dimensions. Consistent with this SR-like result for the source tensor, Nordstrom and independently, Schrodinger, found for three spatial dimensions that the Einstein gravitational energy-momentum pseudo-tensor vanished in proper quasi-rectangular coordinates. The present work shows that this vanishing holds for the pseudo-tensor when extended to n spatial dimensions. Two additional consequences of this work are: 1) the dependency of the Einstein gravitational coupling constant κ on spatial dimensionality employed earlier is further justified;2) the Tolman expression for the mass of a static, isolated system is generalized to take into account the dimensionality of space for n ≥ 3.

Exciton Bose–Einstein Condensation in Transition Metal Dichalcogenide Monolayer under In-Plane Magnetic Fields

Based on the Gross–Pitaevskii equation,we theoretically investigate exciton Bose–Einstein condensation(BEC)in transition metal dichalcogenide monolayers(TMDC-MLs)under in-plane magnetic fields.We observe that the in-plane magnetic fields exert a strong influence on the exciton BEC wave functions in TMDC-MLs because of the mixing of the bright and dark exciton states via Zeeman effect.This leads to the brightening of the dark exciton BEC states.The competition between the dipole–dipole interactions caused by the long-range Coulomb interaction and the Zeeman effect induced by the in-plane magnetic fields can effectively regulate dark exciton BEC states.Our findings emphasize the utility of TMD-MLs as platforms for investigating collective phenomenon involving excited states.

Maxwell Demon and Einstein–Podolsky–Rosen Steering

Research of Maxwell demon and quantum entanglement is important because of its foundational significance in physics and its potential applications in quantum information. Previous studies on the Maxwell demon have primarily focused on thermodynamics, taking into account quantum correlations. Here we consider from another perspective and ask whether quantum non-locality correlations can be simulated by performing work. The Maxwell demon-assisted Einstein–Podolsky–Rosen(EPR) steering is thus proposed, which implies a new type of loophole. The application of Landauer's erasure principle suggests that the only way to close this loophole during a steering task is by continuously monitoring the heat fluctuation of the local environment by the participant.We construct a quantum circuit model of Maxwell demon-assisted EPR steering, which can be demonstrated by current programmable quantum processors, such as superconducting quantum computers. Based on this quantum circuit model, we obtain a quantitative formula describing the relationship between energy dissipation due to the work of the demon and quantum non-locality correlation. The result is of great physical interest because it provides a new way to explore and understand the relationship between quantum non-locality, information, and thermodynamics.

Rydberg-Induced Topological Solitons in Three-Dimensional Rotation Spin–Orbit-Coupled Bose–Einstein Condensates

We present a novel approach for generating stable three-dimensional(3D)spatiotemporal solitons(SSs)within a rotating Bose–Einstein condensate,incorporating spin–orbit coupling(SOC),a weakly anharmonic potential and cold Rydberg atoms.This intricate system facilitates the emergence of quasi-stable 3D SSs with topological charges|m|≤3 in two spinor components,potentially exhibiting diverse spatial configurations.Our findings reveal that the Rydberg long-range interaction,spin–orbit coupling,and rotational angular frequency exert significant influence on the domains of existence and stability of these solitons.Notably,the Rydberg interaction contributes to a reduction in the norm of topological solitons,while the SOC plays a key role in stabilizing the SSs with finite topological charges.This research of SSs exhibits potential applications in precision measurement,quantum information processing,and other advanced technologies.

Dynamics of Ring Dark Solitons and the Following Vortices in Spin-1 Bose–Einstein Condensates

This work focuses on the evolution behaviors of ring dark solitons(RDSs) and the following vortices after the collapses of RDSs in spin-1 Bose–Einstein condensates. We find that the weighted average of the initial depths of three components determines the number and motion trajectories of vortex dipoles. For the weighted average of the initial depths below the critical depth, two vortex dipoles form and start moving along the horizontal axis.For the weighted average depth above the critical depth, two or four vortex dipoles form, and all start moving along the vertical axis. For the RDS with weighted average depth at exactly the critical point, four vortex dipoles form, half of the vortex dipoles initiate movement vertically, and the other half initiate movement horizontally.Our conclusion is applicable to the two-component system studied in earlier research, indicating its universality.

Dissipation-Driven Superradiant Phase Transition of a Two-Dimensional Bose-Einstein Condensate in a Double Cavity

We study superradiant phase transitions in a hybrid system of a two-dimensional Bose–Einstein condensate of atoms and two cavities arranged with a tilt angle.By adjusting the loss rate of cavities,we map out the phase diagram of steady states within a mean field framework.It is found that when the loss rates of the two cavities are different,superradiant transitions may not occur at the same time in the two cavities.A first-order phase transition is observed between the states with only one cavity in superradiance and both in superradiance.In the case that both cavities are superradiant,a net photon current is observed flowing from the cavity with small decay rate to the one with large decay rate.The photon current shows a non-monotonic dependence on the loss rate difference,owing to the competition of photon number difference and cavity field phase difference.Our findings can be realized and detected in experiments.

Proposal for a realtime Einstein-synchronization-defined satellite virtual clock

Realization of high performance satellite onboard clock is vital for various positioning, navigation, and timing applications. For further improvement of the synchronization-based satellite time and frequency references, we propose a geosynchronous(GEO) satellite virtual clock concept based on ground–satellite synchronization and present a beacon transponder structure for its implementation(scheduled for launch in 2025), which does not require atomic clocks to be mounted on the satellite. Its high performance relies only on minor modifications to the existing transponder structure of GEO satellites. We carefully model the carrier phase link and analyze the factors causing link asymmetry within the special relativity. Considering that performance of such synchronization-based satellite clocks is primarily limited by the link's random phase noise, which cannot be adequately modeled, we design a closed-loop experiment based on commercial GEO satellites for pre-evaluation. This experiment aims at extracting the zero-means random part of the ground-satellite Ku-band carrier phase via a feedback loop. Ultimately, we obtain a 1σ value of 0.633 ps(two-way link), following the Gaussian distribution. From this result, we conclude that the proposed real-time Einstein-synchronization-defined satellite virtual clock can achieve picosecond-level replication of onboard time and frequency.

Kármán vortex street in a spin–orbit-coupled Bose–Einstein condensate with PT symmetry

The dynamics of spin–orbit-coupled Bose–Einstein condensate with parity-time symmetry through a moving obstacle potential is simulated numerically. In the miscible two-component condensate, the formation of the Kármán vortex street is observed in one component, while ‘the half-quantum vortex street' is observed in the other component. Other patterns of vortex shedding, such as oblique vortex dipoles, V-shaped vortex pairs, irregular turbulence, and combined modes of various wakes, can also be found. The ratio of inter-vortex spacing in one row to the distance between vortex rows is approximately0.18, which is less than the stability condition 0.28 of classical fluid. The drag force acting on the obstacle potential is simulated. The parametric regions of Kármán vortex street and other vortex patterns are calculated. The range of Kármán vortex street is surrounded by the region of combined modes. In addition, spin–orbit coupling disrupts the symmetry of the system and the gain-loss affects the local particle distribution of the system, which leads to the local symmetry breaking of the system, and finally influences the stability of the Kármán vortex street. Finally, we propose an experimental protocol to realize the Kármán vortex street in a system.

基于Einstein算子的直觉模糊值相似度及其在聚类中的应用

基于直觉模糊等价矩阵聚类的关键在于合理构建样本之间的直觉模糊值相似度,这种相似度是有2个分量的二元形式,其中一个分量代表着2个对象之间的相似程度,另一个代表非相似程度.提出一种基于Einstein算子的直觉模糊值相似度构造方法并将其应用到聚类分析.首先,给出Einstein算子诱导的直觉模糊剩余蕴含,并通过聚合直觉模糊剩余蕴含得到直觉模糊值相似度;然后,利用这种直觉模糊值相似度构建直觉模糊相似矩阵,并通过直觉模糊相似矩阵的合成运算得到直觉模糊等价矩阵,进而给出直觉模糊聚类算法;最后,通过算例对该方法进行说明和分析.

Solving the Olbers’s Paradox, Explaining the “Red-Shift”, and Challenging the Relativities by “Sun Matters Theory” and “Sun Model of Universe”, an Evolution of the Einstein’s Static Universe Model

Olbers’s paradox, known as the dark night paradox, is an argument in astrophysics that the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe. Big-Bang theory was used to partially explain this paradox, while introducing new problems. Hereby, we propose a better theory, named Sun Matters Theory, to explain this paradox. Moreover, this unique theory supports and extended the Einstein’s static universe model proposed by Albert Einstein in 1917. Further, we proposed our new universe model, “Sun Model of Universe”. Based on the new model and novel theory, we generated innovative field equation by upgrading Einstein’s Field Equation through adding back the cosmological constant, introducing a new variable and modifying the gravitationally-related concepts. According to the Sun Model of Universe, the dark matter and dark energy comprise the so-called “Sun Matters”. The observed phenomenon like the red shift is explained as due to the interaction of ordinary light with Sun Matters leading to its energy and frequency decrease. In Sun Model, our big universe consists of many universes with ordinary matter at the core mixed and surrounded with the Sun Matters. In those universes, the laws of physics may be completely or partially different from that of our ordinary universe with parallel civilizations. The darkness of night can be easily explained as resulting from the interaction of light with the Sun Matters leading to the sharp decrease in the light intensity. Sun Matters also scatter the light from a star, which makes it shining as observed by Hubble. Further, there is a kind of Sun Matters named “Sun Waters”, surrounding every starts. When lights pass by the sun, the Sun Waters deflect the lights to bend the light path. According to the Sun Model, it is the light bent not the space bent that was proposed in the theory of relativities.

单压吸收式Einstein循环制冷机中气泡泵参数的设计确定

提出了在制冷循环初始运行工况和设计蒸发冷量已知条件下单压吸收式Einstein循环制冷机中气泡泵尺寸参数的理论计算方法,并给出了算例。计算过程和算例结果对该类制冷机的整体设计提供了参考。

单压吸收式Einstein循环制冷机中气泡泵的性能分析

单压吸收式Einstein循环制冷机中的细管径气泡泵是系统的主要驱动装置,作用在于提升发生器内的稀氨水工质至高位贮液器;气泡泵的最佳运行状态不是由提升管高度决定的,而是在很大程度上取决于沉浸比和泵管的内径尺寸参数。所以针对气泡泵的研究概况,工作原理以及在Einstein制冷循环中的运行机理做了简单的介绍,并根据气液两相流压降理论得出了固定提升效率下气泡泵内径、沉浸比和外部加热功率三者的性能关系曲线,为气泡泵的设计提供了数据参照。

Einstein制冷循环中气泡泵的试验研究

通过自行设计的可视化气泡泵实验装置,以氨水工质为研究对象,针对不同实验工况条件下的气泡泵的性能进行了实验研究。实验结果表明:气泡泵的液体流量随着提升管管径,沉浸比和加热功率有关,并且随着沉浸比和加热功率的增加而增大;沉浸比的增大而增大;气泡泵的效率也与沉浸比和加热功率有密切的关系:气泡泵的效率随着沉浸比的增加而增加,随着加热功率的增加表现为减小的趋势。

单压吸收式Einstein循环制冷机的设计

介绍了单压吸收式Einstein循环制冷机的设计方案,阐述了制冷机的组成、工作原理及主要部分的设计说明。

Einstein推移质公式探讨

本文从多方面对Einstein推移质公式进行修正.首先基于时间连续、状态离散的Markov过程严格推导公式结构,具有物理概念清楚、数学处理严密的特点;其次取无因次单步距离和单步运动时间均为水流强度参数的函数,使之更符合现象的物理性质.此外,起动概率公式不仅考虑到推移力作用并取脉动底速遵循正态分布,理论上较为完善;而且积分限系数全由以往成果预先确定,因而可视为独立的理论公式.经上述修正的推移质公式与试验资料符合良好,可供计算应用.

Einstein制冷系统气泡泵理论模型修正验证研究

基于漂移流模型理论建立了气泡泵理论模型,对Einstein制冷系统中气泡泵在绝热弹状流下的提升特性进行理论分析,并以饱和纯水为工质对气泡泵稳态性能进行实验研究。根据气泡泵性能参数的实验值和理论计算值,采用最小二乘法对气泡泵阻力损失系数进行拟合,对气泡泵理论模型进行修正并得到相应的实验关联式,并对该关联式的可信度进行验证。结果表明:实验结果与理论修正结果吻合性较好,误差在5.3%以内,修正结果具有较强准确性和可行性,完善了气泡泵理论模型。为气泡泵的优化设计提供理论指导,对进一步研究Einstein制冷系统气泡泵性能具有重要参考价值。

Einstein谜的SAT求解

Einstein谜,亦称Zebra谜,是爱因斯坦在20世纪初提出的,他说世界上有98%的人答不出来。该问题是一个典型的逻辑推理题,可以通过SAT求解给出问题的答案。现将Einstein谜转换成SAT求解问题,并使用当前流行的SAT求解器,如MinSat,对Einstein谜进行自动求解。

基于Einstein算子的证据冲突度量方法

为了有效度量融合证据之间的冲突,在分析冲突因子和典型证据冲突度量方法不足的基础上,提出了一种基于Einstein算子的证据冲突度量方法。首先,利用证据向量度量思想给出证据之间的差异度矩阵,并定义对数形式的差异因子;然后,引入模糊集相似关系定义证据之间的相关系数;最后,综合考虑证据之间的差异性和相关性,利用Einstein算子定义一种新的证据冲突度量因子。仿真实验结果表明:该方法不但可以有效度量证据之间的冲突程度,而且对冲突证据的融合具有良好的收敛性。