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Revisiting Legendre transformations in Finsler geometry 重温芬斯勒几何中的勒让德变换
IF 1.8 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-03-05 DOI: 10.1142/s021988782450155x
Ernesto Rodrigues, Iarley P. Lobo

In this paper, we discuss the conditions for mapping the geometric description of the kinematics of particles that probe a given Hamiltonian in phase space to a description in terms of Finsler geometry (and vice-versa).

在本文中,我们讨论了将相空间中探测给定哈密顿的粒子运动学的几何描述映射到芬斯勒几何描述(反之亦然)的条件。
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引用次数: 0
A note on generalized weakly ℋ-symmetric manifolds and relativistic applications 关于广义弱ℋ对称流形和相对论应用的说明
IF 1.8 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-02-29 DOI: 10.1142/s0219887824501536
Sameh Shenawy, Nasser Bin Turki, Carlo Mantica

In this work, generalized weakly -symmetric space-times (GWHS)n are investigated, where is any symmetric (0,2) tensor. It is proved that, in a nontrivial (GWHS)n space-time, the tensor has a perfect fluid form. Accordingly, sufficient conditions for a nontrivial generalized weakly Ricci symmetric space-time (GWRS)n to be either an Einstein space-time or a perfect fluid space-time are obtained. Also, conditions for space-times admitting either a generalized weakly symmetric energy-momentum tensor or a generalized weakly symmetric 𝒵 tensor to be Einstein or perfect fluid space-times are provided.

本文研究了广义弱ℋ对称时空(GWHS)n,其中ℋ是任意对称(0,2)张量。研究证明,在非微观(GWHS)n 时空中,张量ℋ具有完美的流体形式。相应地,得到了非微观广义弱里奇对称时空(GWRS)n 成为爱因斯坦时空或完美流体时空的充分条件。此外,还提供了包含广义弱对称能动张量或广义弱对称𝒵张量的时空成为爱因斯坦时空或完美流体时空的条件。
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引用次数: 0
Observation constraints on scalar field cosmological model in anisotropic universe 各向异性宇宙中标量场宇宙学模型的观测约束
IF 1.8 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-02-29 DOI: 10.1142/s0219887824501445
Vinod Kumar Bhardwaj, Anil Kumar Yadav
<p>In this study, we have explored a scalar field cosmological model in the axially symmetric Bianchi type-I universe. In this study, our aim is to constrain the scalar field dark energy model in an anisotropic background. For this purpose, the explicit solution of the developed field equations for the model is determined and analyzed. Constraints on the cosmological model parameters are established utilizing Markov Chain Monte Carlo (MCMC) analysis and using the latest observational datasets of OHD, BAO, and Pantheon. For the combined dataset (OHD, BAO, and Pantheon), the best-fit values of Hubble and density parameters are estimated as <span><math altimg="eq-00001.gif" display="inline" overflow="scroll"><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>7</mn><mn>1</mn><mo>.</mo><mn>5</mn><mn>4</mn><mo stretchy="false">±</mo><mn>0</mn><mo>.</mo><mn>2</mn><mn>8</mn></math></span><span></span>, <span><math altimg="eq-00002.gif" display="inline" overflow="scroll"><msub><mrow><mi mathvariant="normal">Ω</mi></mrow><mrow><mi>m</mi><mn>0</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn><mn>6</mn><mn>2</mn><mn>2</mn><mo stretchy="false">±</mo><mn>0</mn><mo>.</mo><mn>0</mn><mn>0</mn><mn>2</mn><mn>1</mn></math></span><span></span><span><math altimg="eq-00003.gif" display="inline" overflow="scroll"><msub><mrow><mi mathvariant="normal">Ω</mi></mrow><mrow><mi>ϕ</mi><mn>0</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>7</mn><mn>3</mn><mn>3</mn><mn>1</mn><mo stretchy="false">±</mo><mn>0</mn><mo>.</mo><mn>0</mn><mn>0</mn><mn>4</mn><mn>6</mn></math></span><span></span> and <span><math altimg="eq-00004.gif" display="inline" overflow="scroll"><msub><mrow><mi mathvariant="normal">Ω</mi></mrow><mrow><mi>σ</mi><mn>0</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>0</mn><mn>0</mn><mn>0</mn><mn>1</mn><mn>6</mn><mn>2</mn><mo stretchy="false">±</mo><mn>0</mn><mo>.</mo><mn>0</mn><mn>0</mn><mn>0</mn><mn>0</mn><mn>6</mn><mn>3</mn></math></span><span></span>. The model shows a flipping nature and redshift transition occurs at <span><math altimg="eq-00005.gif" display="inline" overflow="scroll"><msub><mrow><mi>z</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>6</mn><mn>9</mn><mn>6</mn><msubsup><mrow><mn>4</mn></mrow><mrow><mo stretchy="false">−</mo><mn>0</mn><mo>.</mo><mn>0</mn><mn>0</mn><mn>0</mn><mn>6</mn></mrow><mrow><mo stretchy="false">+</mo><mn>0</mn><mo>.</mo><mn>0</mn><mn>1</mn><mn>3</mn><mn>6</mn></mrow></msubsup></math></span><span></span>, and the present value of decelerated parameter is computed to be <span><math altimg="eq-00006.gif" display="inline" overflow="scroll"><msub><mrow><mi>q</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mo stretchy="false">−</mo><mn>0</mn><mo>.</mo><mn>6</mn><mn>9</mn><mn>6</mn><mn>4</mn><mo stretchy="false">±</mo><mn>0</mn><mo>.</mo><mn>0</mn><mn>2</mn><mn>8</mn></math></span><span></span> for the combined dataset. We have explored characteristics like the univ
在这项研究中,我们探索了轴对称比安奇 I 型宇宙中的标量场宇宙学模型。在这项研究中,我们的目的是在各向异性背景下约束标量场暗能量模型。为此,我们确定并分析了模型场方程的显式解。利用马尔可夫链蒙特卡罗(MCMC)分析和最新的 OHD、BAO 和 Pantheon 观测数据集,建立了对宇宙学模型参数的约束。对于组合数据集(OHD、BAO 和 Pantheon),哈勃和密度参数的最佳拟合值估计为 H0=71.54±0.28,Ωm0=0.2622±0.0021Ωj0=0.7331±0.0046,Ωσ0=0.000162±0.000063。该模型具有翻转性质,红移转变发生在zt=0.6964-0.0006+0.0136,综合数据集计算出的减速参数现值为q0=-0.6964±0.028。我们探索了宇宙的年龄、粒子视界、减速参数和抽搐参数等特征。我们分析并展示了能量密度ρj、标量场压力pj和状态方程参数ωj等动力学特性。我们还描述了标量势 V(ϕ) 和标量场的行为。此外,作者还描述了标量张量宇宙学中能量条件的行为。标量场的贡献描述了目前宇宙加速膨胀的情景。
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For the combined dataset (OHD, BAO, and Pantheon), the best-fit values of Hubble and density parameters are estimated as &lt;span&gt;&lt;math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo stretchy=\"false\"&gt;±&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;, &lt;span&gt;&lt;math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi mathvariant=\"normal\"&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=\"false\"&gt;±&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;&lt;span&gt;&lt;math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi mathvariant=\"normal\"&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=\"false\"&gt;±&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; and &lt;span&gt;&lt;math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi mathvariant=\"normal\"&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo stretchy=\"false\"&gt;±&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;. The model shows a flipping nature and redshift transition occurs at &lt;span&gt;&lt;math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;−&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;+&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;, and the present value of decelerated parameter is computed to be &lt;span&gt;&lt;math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo stretchy=\"false\"&gt;−&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo stretchy=\"false\"&gt;±&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; for the combined dataset. We have explored characteristics like the univ","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"84 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
From the classical Frenet–Serret apparatus to the curvature and torsion of quantum-mechanical evolutions. Part I. Stationary Hamiltonians 从经典的 Frenet-Serret 装置到量子力学演化的曲率和扭转。第一部分:静态哈密顿
IF 1.8 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-02-29 DOI: 10.1142/s0219887824501524
Paul M. Alsing, Carlo Cafaro
<p>It is known that the Frenet–Serret apparatus of a space curve in three-dimensional Euclidean space determines the local geometry of curves. In particular, the Frenet–Serret apparatus specifies important geometric invariants, including the curvature and the torsion of a curve. It is also acknowledged in quantum information science that low complexity and high efficiency are essential features to achieve when cleverly manipulating quantum states that encode quantum information about a physical system.</p><p>In this paper, we propose a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by dynamically evolving state vectors. Specifically, we propose a quantum version of the Frenet–Serret apparatus for a quantum trajectory in projective Hilbert space traced by a parallel-transported pure quantum state evolving unitarily under a stationary Hamiltonian specifying the Schrödinger equation. Our proposed constant curvature coefficient is given by the magnitude squared of the covariant derivative of the tangent vector <span><math altimg="eq-00001.gif" display="inline" overflow="scroll"><mo>|</mo><mi>T</mi><mo stretchy="false">〉</mo></math></span><span></span> to the state vector <span><math altimg="eq-00002.gif" display="inline" overflow="scroll"><mo>|</mo><mi mathvariant="normal">Ψ</mi><mo stretchy="false">〉</mo></math></span><span></span> and represents a useful measure of the bending of the quantum curve. Our proposed constant torsion coefficient, instead, is defined in terms of the magnitude squared of the projection of the covariant derivative of the tangent vector <span><math altimg="eq-00003.gif" display="inline" overflow="scroll"><mo>|</mo><mi>T</mi><mo stretchy="false">〉</mo></math></span><span></span>, orthogonal to both <span><math altimg="eq-00004.gif" display="inline" overflow="scroll"><mo>|</mo><mi>T</mi><mo stretchy="false">〉</mo></math></span><span></span> and <span><math altimg="eq-00005.gif" display="inline" overflow="scroll"><mo>|</mo><mi mathvariant="normal">Ψ</mi><mo stretchy="false">〉</mo></math></span><span></span>. The torsion coefficient provides a convenient measure of the twisting of the quantum curve. Remarkably, we show that our proposed curvature and torsion coefficients coincide with those existing in the literature, although introduced in a completely different manner. Interestingly, not only we establish that zero curvature corresponds to unit geodesic efficiency during the quantum transportation in projective Hilbert space, but we also find that the concepts of curvature and torsion help enlighten the statistical structure of quantum theory. Indeed, while the former concept can be essentially defined in terms of the concept of kurtosis, the positivity of the latter can be regarded as a restatement of the well-known Pearson inequality that involves both the concepts of kurtosis and skewness in mathematical statistics. Finally, not only do we present illustrative examples with no
众所周知,三维欧几里得空间中空间曲线的 Frenet-Serret 装置决定了曲线的局部几何。特别是,Frenet-Serret 装置规定了重要的几何不变式,包括曲线的曲率和扭转。量子信息科学领域也承认,在巧妙地操纵编码物理系统量子信息的量子态时,低复杂度和高效率是必须实现的基本特征。在本文中,我们从几何角度提出了如何量化由动态演化的状态矢量追踪的量子曲线的弯曲和扭曲。具体地说,我们提出了一种量子版的 Frenet-Serret 装置,该装置适用于投影希尔伯特空间中的量子轨迹,该轨迹由在指定薛定谔方程的静态哈密尔顿下单元化演化的平行传输纯量子态追踪。我们提出的恒定曲率系数由切线向量|T〉到状态向量|Ψ〉的协变导数的平方给出,是量子曲线弯曲程度的有效度量。而我们提出的恒定扭转系数,是以切线向量|T〉的协变导数投影的大小平方来定义的,与|T〉和|Ψ〉都正交。扭转系数为量子曲线的扭转提供了方便的度量。值得注意的是,我们证明了我们提出的曲率系数和扭转系数与文献中已有的系数不谋而合,尽管引入的方式完全不同。有趣的是,我们不仅确定了零曲率对应于投影希尔伯特空间量子传输过程中的单位大地效率,还发现曲率和扭转的概念有助于揭示量子理论的统计结构。事实上,前一个概念本质上可以用峰度概念来定义,而后一个概念的正向性则可以看作是对著名的皮尔逊不等式的重述,它同时涉及数理统计中的峰度和偏度概念。最后,我们不仅举例说明了不可能产生扭转的单量子比特时间无关哈密顿演化的非零曲率,还讨论了扩展到双量子比特静态哈密顿的物理应用,这些哈密顿会产生由具有不同纠缠程度的量子态(从可分离态到最大纠缠的贝尔态)追踪的既有非零曲率又有非消失扭转的曲线。在附录 C 中,我们研究了在量子海森堡汉密尔顿演化下三个量子比特|GHZ〉和|W〉态的不同曲率和扭转特性。
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引用次数: 0
The equivalence principle as a Noether symmetry 作为诺特对称性的等价原理
IF 1.8 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-02-29 DOI: 10.1142/s0219887824400140
Salvatore Capozziello, Carmen Ferrara

The equivalence principle is considered in the framework of metric-affine gravity. We show that it naturally emerges as a Noether symmetry starting from a general non-metric theory. In particular, we discuss the Einstein equivalence principle and the strong equivalence principle showing their relations with the non-metricity tensor. Possible violations are also discussed pointing out the role of non-metricity in this debate.

等价原理是在度量-非线性引力框架下考虑的。我们证明,从一般非度量理论出发,等价原理自然会作为诺特对称性出现。我们特别讨论了爱因斯坦等价原理和强等价原理,展示了它们与非度量张量的关系。我们还讨论了可能出现的违反情况,指出了非度量性在这场辩论中的作用。
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引用次数: 0
Solitons and traveling waves structure for the Schrödinger–Hirota model in fluids 流体中薛定谔-希罗塔模型的孤子和行波结构
IF 1.8 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-02-23 DOI: 10.1142/s0219887824501457
Fazal Badshah, Kalim U. Tariq, Jian-Guo Liu, S. M. Raza Kazmi

The Schrödinger–Hirota equation is one of the most important models of contemporary physics which is popular throughout the broad fields of fluid movement as well as in the study of thick-water crests, liquid science, refractive optical components and so on. In this paper, we utilize the Hirota bilinear technique and the unified technique to attain various soliton solutions of the governing model analytically. These approaches are robust, powerful and unique also have many applications in different fields of mathematical physics. The solutions attained from these techniques are highly valuable and useful in various fields of sciences specially in the transmissions of optical fibers, also they give different behaviors including V-shaped and periodic soliton solution behavior. Further, the approaches applied here are not applied in this model previously. Therefore, ours is a new work, which summarizes its novelty. The 3D, 2D and contour plots are included to grasp the understanding of solutions’ behavior. These findings are valuable in electronic communications such as elliptical circuits and in investigation of solitude controlling.

薛定谔-广达方程是当代物理学中最重要的模型之一,在流体运动的广泛领域以及浓水波峰、液体科学、折射光学元件等研究中广为流行。在本文中,我们利用 Hirota 双线性技术和统一技术,通过分析获得了支配模型的各种孤子解。这些方法稳健、强大、独特,在数学物理的不同领域也有很多应用。从这些技术中获得的解在各个科学领域,特别是光纤传输领域,具有很高的价值和实用性,而且它们还给出了不同的行为,包括 V 形和周期性孤子解行为。此外,这里应用的方法以前从未应用于该模型。因此,我们的研究是一项新工作,总结了其新颖性。为了理解解的行为,我们绘制了三维、二维和等值线图。这些发现对椭圆电路等电子通信和孤独控制研究很有价值。
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引用次数: 0
Spacetime metric from quantum-gravity corrected Feynman propagators 来自量子引力修正费曼传播子的时空度量
IF 1.8 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-02-23 DOI: 10.1142/s0219887824501391
P. Fernández de Córdoba, J. M. Isidro, Rudranil Roy

Differentiation of the scalar Feynman propagator with respect to the spacetime coordinates yields the metric on the background spacetime that the scalar particle propagates in. Now Feynman propagators can be modified in order to include quantum-gravity corrections as induced by a zero-point length L>0. These corrections cause the length element s2 to be replaced with s2+4L2 within the Feynman propagator. In this paper, we compute the metrics derived from both the quantum-gravity free propagators and from their quantum-gravity corrected counterparts. We verify that the latter propagators yield the same spacetime metrics as the former, provided one measures distances greater than the quantum of length L. We perform this analysis in the case of the background spacetime D in the Euclidean sector.

将标量费曼传播子与时空坐标微分,就可以得到标量粒子在其中传播的背景时空的度量。现在,可以对费曼传播子进行修改,以便包含零点长度 L>0 所引起的量子引力修正。这些修正会导致费曼传播子中的长度元素 s2 被替换为 s2+4L2。在本文中,我们计算了无量子引力传播子及其量子引力修正传播子的度量。我们在欧几里得扇区的背景时空ℝD 的情况下进行了这一分析。
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引用次数: 0
Conformal η-Ricci–Bourguignon soliton in general relativistic spacetime 广义相对论时空中的共形 η-Ricci-Bourguignon 孤子
IF 1.8 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-02-23 DOI: 10.1142/s0219887824501482
Santu Dey, Shyamal Kumar Hui, Soumendu Roy, Ali H. Alkhaldi

In this research paper, we determine the nature of conformal η-Ricci–Bourguignon soliton on a general relativistic spacetime with torse forming potential vector field. Besides this, we evaluate a specific situation of the soliton when the spacetime admitting semi-symmetric energy–momentum tensor with respect to conformal η-Ricci–Bourguignon soliton, whose potential vector field is torse-forming. Next, we explore some characteristics of curvature on a spacetime that admits conformal η-Ricci–Bourguignon soliton. In addition, we turn up some physical perception of dust fluid, dark fluid and radiation era in a general relativistic spacetime in terms of conformal η-Ricci–Bourguignon soliton. Finally, we examine necessary and sufficient conditions for a 1-form η, which is the g-dual of the vector field ξ on general relativistic spacetime to be a solution of the Schrödinger–Ricci equation.

在这篇研究论文中,我们确定了在具有矩形势向量场的一般相对论时空中的共形η-里奇-布尔古尼孤子的性质。此外,我们还评估了在共形η-里奇-布尔吉尼孤子的半对称能动张量时空中孤子的具体情况,其势矢场是环形的。接下来,我们探讨了共形 η-Ricci-Bourguignon 孤子所在时空的一些曲率特征。此外,我们还从共形η-里奇-布尔基尼孤子的角度提出了广义相对论时空中尘埃流体、暗流体和辐射时代的一些物理概念。最后,我们研究了1-形式η成为薛定谔-里奇方程的解的必要条件和充分条件,η是广义相对论时空中矢量场ξ的g二元。
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引用次数: 0
Lie symmetries of Lemaitre–Tolman–Bondi metric 勒梅特-托尔曼-邦迪公设的李对称性
IF 1.8 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-02-22 DOI: 10.1142/s0219887824501329
Jamshed Khan, Tahir Hussain, Ashfaque H. Bokhari, Muhammad Farhan

The aim of this paper is to investigate Lie symmetries including Killing, homothetic and conformal symmetries of Lemaitre–Tolman–Bondi (LTB) spacetime metric. To find all LTB metrics admitting these three types of symmetries, we have analyzed the set of symmetry equations by a Maple algorithm that provides some restrictions on the functions involved in LTB metric under which this metric admits the three mentioned symmetries. The solution of symmetry equations under these restrictions leads to the explicit form of symmetries. The stress–energy tensor is calculated for all the obtained metrics in order to discuss their physical significance. It is noticed that most of these metrics satisfy certain energy conditions and correspond to anisotropic fluids.

本文旨在研究列对称性,包括勒梅特-托尔曼-邦迪(LTB)时空度量的基林对称性、同调对称性和共形对称性。为了找到所有承认这三种对称性的 LTB 公设,我们通过 Maple 算法分析了对称方程组,该算法对 LTB 公设中涉及的函数提供了一些限制,在这些限制下,该公设承认上述三种对称性。在这些限制条件下求解对称方程可以得到对称的显式形式。为了讨论它们的物理意义,我们计算了所有得到的度量的应力能量张量。我们注意到,这些度量大多满足一定的能量条件,并与各向异性流体相对应。
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引用次数: 0
The geometry of quantum computing 量子计算的几何学
IF 1.8 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-02-22 DOI: 10.1142/s0219887824400115
E. Ercolessi, R. Fioresi, T. Weber

In this expository paper, we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we focus on quantum information geometry and ZX-calculus, establishing a connection between quantum computing questions and quantum groups, i.e. Hopf algebras.

在这篇阐述性论文中,我们简要介绍了一些量子计算问题的几何建模。在简要介绍术语之后,我们重点讨论量子信息几何和 ZX 计算,建立量子计算问题与量子群(即霍普夫代数)之间的联系。
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引用次数: 0
期刊
International Journal of Geometric Methods in Modern Physics
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