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Anisotropic Spheres with Tolman–Kuchowicz Spacetime in the Context of f ( Q , T ) $f(Q,T)$ Gravity f ( Q , T ) $f(Q,T)$ 重力背景下具有托尔曼-库霍维奇时空的各向异性球体
IF 2.2 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-10-03 DOI: 10.1002/andp.202400233
Chaitra Chooda Chalavadi, V. Venkatesha, H Aruna Kumara
{"title":"Anisotropic Spheres with Tolman–Kuchowicz Spacetime in the Context of \u0000 \u0000 \u0000 f\u0000 (\u0000 Q\u0000 ,\u0000 T\u0000 )\u0000 \u0000 $f(Q,T)$\u0000 Gravity","authors":"Chaitra Chooda Chalavadi,&nbsp;V. Venkatesha,&nbsp;H Aruna Kumara","doi":"10.1002/andp.202400233","DOIUrl":"https://doi.org/10.1002/andp.202400233","url":null,"abstract":"<p>This study primarily focuses on exploring the nature of anisotropic spheres within the framework of extended symmetric teleparallel gravity. To accomplish this, an anisotropic matter distribution for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>(</mo>\u0000 <mi>Q</mi>\u0000 <mo>,</mo>\u0000 <mi>T</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$f(Q,T)$</annotation>\u0000 </semantics></math> gravity model with Tolman–Kuchowicz spacetime is considered. Through this analysis, the necessary conditions for matching the interior and exterior geometries of the spheres are discussed and calculated the values of the unknown parameters involved. Furthermore, the physical properties of these spheres are analyzed using observational data from compact objects. The results demonstrate that the interior solutions obtained for anisotropic spheres fulfill all requisite physical criteria, thereby ensuring the stability of our model.</p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"536 11","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142664627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Quantum Verification for a Class of n $n$ -Qubit Quantum Entangled States
IF 2.2 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-10-03 DOI: 10.1002/andp.202400305
Yangwei Ou, Xiaoqing Tan, Daipengwei Bao, Qingshan Xu, Qin Li, Shao-Ming Fei
{"title":"Quantum Verification for a Class of \u0000 \u0000 n\u0000 $n$\u0000 -Qubit Quantum Entangled States","authors":"Yangwei Ou,&nbsp;Xiaoqing Tan,&nbsp;Daipengwei Bao,&nbsp;Qingshan Xu,&nbsp;Qin Li,&nbsp;Shao-Ming Fei","doi":"10.1002/andp.202400305","DOIUrl":"https://doi.org/10.1002/andp.202400305","url":null,"abstract":"<p>The quantum verification is to determine whether a quantum device is intentionally deceptive by assessing the proximity between the actual output state and the expected state. As a crucial step toward the advancement of quantum technology, numerous quantum state verification methods have been proposed. However, there remains a scarcity of methods for verifying states with an arbitrary number of qubits. A verification strategy for the entangled states <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mi>ψ</mi>\u0000 <mo>⟩</mo>\u0000 </mrow>\u0000 <mo>=</mo>\u0000 <mi>sin</mi>\u0000 <mi>θ</mi>\u0000 <msup>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mn>0</mn>\u0000 <mo>⟩</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>⊗</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>+</mo>\u0000 <mi>cos</mi>\u0000 <mi>θ</mi>\u0000 <msup>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mn>1</mn>\u0000 <mo>⟩</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>⊗</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathinner {|{psi }rangle } =sin theta mathinner {|{0}rangle }^{otimes n} +cos theta mathinner {|{1}rangle } ^{otimes n}$</annotation>\u0000 </semantics></math> with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>θ</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>π</mi>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$theta in (0,pi /2)$</annotation>\u0000 </semantics></math> is proposed. Specifically, an average map is introduced and demonstrated that it simplifies the matrix form of the verification strategy while maintaining the verification efficiency. By optimizing the verification strategies, the strategy with local projective measurements is obtained.</p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"537 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143389257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Photon-Assisted Quantum Phase Transitions in a Cavity Optomechanical System with Two Nonlinear Mechanical Modes 具有两种非线性机械模式的腔体光机械系统中的光子辅助量子相变
IF 2.2 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-09-30 DOI: 10.1002/andp.202400179
Deng-Kui Jiang, Rui Zhang, Ying Liu, Le-Man Kuang
{"title":"Photon-Assisted Quantum Phase Transitions in a Cavity Optomechanical System with Two Nonlinear Mechanical Modes","authors":"Deng-Kui Jiang,&nbsp;Rui Zhang,&nbsp;Ying Liu,&nbsp;Le-Man Kuang","doi":"10.1002/andp.202400179","DOIUrl":"https://doi.org/10.1002/andp.202400179","url":null,"abstract":"<p>Photon-assisted quantum phase transitions (QPTs) are studied in a cavity optomechanical system that consists of one optical cavity and two nonlinear mechanical resonators and explore ground-state properties of quantum phases. It is indicated that the cavity mode can induce effective two-phonon tunneling interaction between two mechanical resonators. It is found that QPTs between the localization phase (LP) and delocalization phase (DP) of phonons can happen through tuning the phonon tunneling interaction. It is shown that the photon-assisted QPT is the second order QPT. Ground-state properties of the quantum phases are also investigated. It is indicated that the ground state of the LP is a separable squeezed state while the ground state of the DP is an entangled state. The results open a new way to engineer quantum phases and QPTs in macroscopic mechanical systems and can benefit a wide range of criticality-enhanced quantum sensing applications.</p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"536 11","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142665162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Violating Lorentz Invariance Minimally by the Emergence of Nonmetricity? A Perspective 非对称性的出现最小程度地违反了洛伦兹不变性?透视
IF 2.2 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-09-27 DOI: 10.1002/andp.202400217
Yuri N. Obukhov, Friedrich W. Hehl
{"title":"Violating Lorentz Invariance Minimally by the Emergence of Nonmetricity? A Perspective","authors":"Yuri N. Obukhov,&nbsp;Friedrich W. Hehl","doi":"10.1002/andp.202400217","DOIUrl":"https://doi.org/10.1002/andp.202400217","url":null,"abstract":"<p>Lorentz invariance belongs to the fundamental symmetries of nature. It is basic for the successful Standard Model of Particle Physics. Nevertheless, within the last decades, Lorentz invariance has been repeatedly questioned. In fact, there exist different research programs addressing this problem. It is argued that a most adequate understanding of a possible violation of Lorentz invariance is achieved in the framework of the gauge-theoretic approach to gravity: a non-vanishing <i>nonmetricity</i> of a metric-affine geometry of spacetime heralds the violation of the Lorentz symmetry.</p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"536 11","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142665204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Electromagnetically Induced Transparency-Like on All-Dielectric Metamaterials 全介质超材料上的电磁诱导透明效应
IF 2.2 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-09-26 DOI: 10.1002/andp.202400128
Renxia Ning, Deqi Li, Ziyang Zhao, Yanfei Zhang, Shaobin Liu
{"title":"Electromagnetically Induced Transparency-Like on All-Dielectric Metamaterials","authors":"Renxia Ning,&nbsp;Deqi Li,&nbsp;Ziyang Zhao,&nbsp;Yanfei Zhang,&nbsp;Shaobin Liu","doi":"10.1002/andp.202400128","DOIUrl":"https://doi.org/10.1002/andp.202400128","url":null,"abstract":"<p>In this paper, an all-dielectric metamaterial structure based on 3D printed is studied. The structure is composed of a 2 × 2 array of hollow cylinders. The electromagnetically induced transparency-like (EIT-like) effect is obtained by analyzing its transmission, and the mechanism of EIT-like is analyzed by electromagnetic field distribution. The mechanism of EIT-like is Mie resonance in the structure. The results demonstrate that the all-dielectric metamaterial structure can obtain slow light effect, and the group index is &gt;800. The research results have potential applications in slow light devices, sensing, and detection on microwave communication systems.</p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"536 12","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Quantized Orbital Angular Momentums of Dipolar Magnons and Magnetoelectric Cavity Polaritons 偶极磁振子和磁电腔极化子的量子化轨道角动量
IF 2.2 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-09-26 DOI: 10.1002/andp.202400222
E. O. Kamenetskii
{"title":"Quantized Orbital Angular Momentums of Dipolar Magnons and Magnetoelectric Cavity Polaritons","authors":"E. O. Kamenetskii","doi":"10.1002/andp.202400222","DOIUrl":"https://doi.org/10.1002/andp.202400222","url":null,"abstract":"<p>Magnons are viewed as local deviations from the ordered state. Usually, the spin magnetic moment of magnons is considered. In a 3D-confined structure of a magnetic insulator with magnetodipolar mode (MDM) oscillations, an orbital angular momentum (OAM) as well as a spin angular momentum (SAM) can be observed along a static magnetic field. In such a confined structure as quasi-2D ferrite disk, energy levels of MDM oscillations are quantized. Quantum confinement is characterized by a half-integer internal OAM, which is also associated with a circulating energy flow. The observation of MDM resonances in the 3D-confined structure of a magnetic insulator is due to the interaction of two subsystems: ferromagnetic and electric polarization orders. The coupling states of these two concurrent orders, caused by OAMs, are considered as magnetoelectric (ME) states. The near fields of MDM resonators are characterized by simultaneous violation of time reversal and inversion symmetry. This plays a significant role in the problems of strong light-matter interaction regime and quantum atmosphere. The analysis of SAM and OAM in 3D-confined magnetic insulators becomes very important for the realization of ME meta-atomic structures. Current interest lies in considering such artificial systems as subwavelength ME quantum emitters of electromagnetic radiation.</p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"536 12","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/andp.202400222","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Microwave-to-Optical Conversion and Amplification in Cavity Optomagnonics System 腔体光电磁学系统中的微波到光学转换和放大
IF 2.2 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-09-26 DOI: 10.1002/andp.202400271
Ye-Ting Yan, Da-Wei Wang, Junya Yang, Ling Zhou
{"title":"Microwave-to-Optical Conversion and Amplification in Cavity Optomagnonics System","authors":"Ye-Ting Yan,&nbsp;Da-Wei Wang,&nbsp;Junya Yang,&nbsp;Ling Zhou","doi":"10.1002/andp.202400271","DOIUrl":"https://doi.org/10.1002/andp.202400271","url":null,"abstract":"<p>A scheme to construct microwave-to-optical conversion and amplification using a hybrid cavity optomagnonics system is presented. A yttrium iron garnet (YIG) sphere with nonlinearity couples to optical transverse-electric (TE) and transverse-magnetic (TM) whispering gallery modes and a microwave mode. It is shown that the TM classical mode can control the quantum signals input from the microwave mode transmission into the optical TE mode. Due to the nonlinearity of the YIG sphere as well as effective magnon-optical nondegenerate parametric amplification form interaction, the microwave quantum signals can be amplified and transmitted into the optical TE mode. The current system can function well as a quantum transistor, which is important for constructing a quantum circuit using a cavity optomagnonics system.</p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"536 12","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Space and Time Correlations in Quantum Histories 量子历史中的时空相关性
IF 2.2 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-09-25 DOI: 10.1002/andp.202400203
Leonardo Castellani, Anna Gabetti
{"title":"Space and Time Correlations in Quantum Histories","authors":"Leonardo Castellani,&nbsp;Anna Gabetti","doi":"10.1002/andp.202400203","DOIUrl":"https://doi.org/10.1002/andp.202400203","url":null,"abstract":"<p>The formalism of generalized quantum histories allows a symmetrical treatment of space and time correlations, by taking different traces of the same history density matrix. In this framework, the characterization of spatial and temporal entanglement is revisited. An operative protocol is presented, to map a history state into the ket of a static composite system. It is demonstrated, by examples, how the Leggett–Garg and the temporal Clauser-Horne-Shimony-Holt (CHSH) inequalities can be violated in this approach.</p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"536 11","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142665161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Optical Super-Oscillation Enables Sub-Diffraction Focusing and Super-Resolution Imaging in the Far-Field
IF 2.2 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-09-24 DOI: 10.1002/andp.202400184
Zhu Li, Zhongming Zang, Kuo Hai, Wen Huang, Dongliang Tang
{"title":"Optical Super-Oscillation Enables Sub-Diffraction Focusing and Super-Resolution Imaging in the Far-Field","authors":"Zhu Li,&nbsp;Zhongming Zang,&nbsp;Kuo Hai,&nbsp;Wen Huang,&nbsp;Dongliang Tang","doi":"10.1002/andp.202400184","DOIUrl":"https://doi.org/10.1002/andp.202400184","url":null,"abstract":"<p>Owing to the inherent wave property of light, the resolution of the optical system is constrained by the diffraction limit. Past decades have seen many efforts to break the diffraction limit at the expense of complex near-field manipulation, pre-labeling, or post-processing. However, an optical access for noninvasive sub-diffraction focusing and super-resolution imaging in the far-field that does not pose dependency on evanescent waves or targets is still highly desirable. Optical super-oscillation method based on the superposition of propagating waves offers a possibility to overcome the diffraction limit in the far-field with arbitrary enhanced resolution. This article reviews the recent progress of optical super-oscillation technology, including research about super-oscillation phenomenon, designs of super-oscillatory lenses for sub-diffraction focusing, super-resolution imaging by optical super-oscillation method, and applications in other domains. The shortcoming and prospective advancements of optical super-oscillation technology are also discussed here. It is expected that this review can provide valuable insights for researchers committed to developing optical super-oscillation technology in various fields.</p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"537 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
2D Gauss Diffraction Gratings 二维高斯衍射光栅
IF 2.2 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-09-11 DOI: 10.1002/andp.202400187
D. S. Citrin
{"title":"2D Gauss Diffraction Gratings","authors":"D. S. Citrin","doi":"10.1002/andp.202400187","DOIUrl":"10.1002/andp.202400187","url":null,"abstract":"&lt;p&gt;2D diffraction gratings based on Gauss lattices are a class of nonperiodic lattice in which the sites are located at &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mover&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;̂&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mover&gt;\u0000 &lt;mi&gt;y&lt;/mi&gt;\u0000 &lt;mo&gt;̂&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${bf R}_{j_1,j_2}=j_1^ndhat{bf x} + j_2^ndhat{bf y}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;mtext&gt;…&lt;/mtext&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mtext&gt;…&lt;/mtext&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$j_1,j_2!in ! lbrace ldots, -1,0,1,ldots rbrace$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 ","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"536 11","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/andp.202400187","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142182160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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