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Relative Dynamics of Vortices in Confined Bose--Einstein Condensates 约束玻色-爱因斯坦凝聚态涡旋的相对动力学
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-11 DOI: arxiv-2409.07657
Tomoki Ohsawa
{"title":"Relative Dynamics of Vortices in Confined Bose--Einstein Condensates","authors":"Tomoki Ohsawa","doi":"arxiv-2409.07657","DOIUrl":"https://doi.org/arxiv-2409.07657","url":null,"abstract":"We consider the relative dynamics -- the dynamics modulo rotational symmetry\u0000in this particular context -- of $N$ vortices in confined Bose--Einstein\u0000Condensates (BEC) using a finite-dimensional vortex approximation to the\u0000two-dimensional Gross--Pitaevskii equation. We give a Hamiltonian formulation\u0000of the relative dynamics by showing that it is an instance of the Lie--Poisson\u0000equation on the dual of a certain Lie algebra. Just as in our accompanying work\u0000on vortex dynamics with the Euclidean symmetry, the relative dynamics possesses\u0000a Casimir invariant and evolves in an invariant set, yielding an\u0000Energy--Casimir-type stability condition. We consider three examples of\u0000relative equilibria -- those solutions that are undergoing rigid rotations\u0000about the origin -- with $N=2, 3, 4$, and investigate their stability using the\u0000stability condition.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"22 3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Discrete Euler-Bernoulli Beam Lattices with Beyond Nearest Connections 具有超越最近连接的离散欧拉-伯努利梁网格
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-11 DOI: arxiv-2409.07173
R. G. Edge, E. Paul, K. H. Madine, D. J. Colquitt, T. A. Starkey, G. J. Chaplain
{"title":"Discrete Euler-Bernoulli Beam Lattices with Beyond Nearest Connections","authors":"R. G. Edge, E. Paul, K. H. Madine, D. J. Colquitt, T. A. Starkey, G. J. Chaplain","doi":"arxiv-2409.07173","DOIUrl":"https://doi.org/arxiv-2409.07173","url":null,"abstract":"The propagation of elastic waves on discrete periodic Euler-Bernoulli\u0000mass-beam lattices is characterised by the competition between coupled\u0000translational and rotational degrees-of-freedom at the mass-beam junctions. We\u0000influence the dynamics of this system by coupling junctions with\u0000beyond-nearest-neighbour spatial connections, affording freedom over the\u0000locality of dispersion extrema in reciprocal space, facilitating the emergence\u0000of interesting dispersion relations. A generalised dispersion relation for an\u0000infinite monatomic mass-beam chain, with any integer order combination of\u0000non-local spatial connections, is presented. We demonstrate that competing\u0000power channels, between mass and rotational inertia, drive the position and\u0000existence of zero group velocity modes within the first Brillouin zone.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"37 8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Deviations from maximal entanglement for eigenstates of the Sachdev-Ye-Kitaev model 萨克德夫-叶-基塔耶夫模型特征状态的最大纠缠偏差
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-11 DOI: arxiv-2409.07043
Yichen Huang, Yi Tan, Norman Y. Yao
{"title":"Deviations from maximal entanglement for eigenstates of the Sachdev-Ye-Kitaev model","authors":"Yichen Huang, Yi Tan, Norman Y. Yao","doi":"arxiv-2409.07043","DOIUrl":"https://doi.org/arxiv-2409.07043","url":null,"abstract":"We consider mid-spectrum eigenstates of the Sachdev-Ye-Kiteav (SYK) model. We\u0000prove that for subsystems whose size is a constant fraction of the system size,\u0000the entanglement entropy deviates from the maximum entropy by at least a\u0000positive constant. This result highlights the difference between the\u0000entanglement entropy of mid-spectrum eigenstates of the SYK model and that of\u0000random states.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"419 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence of higher degree minimizers in the magnetic skyrmion problem 磁天幕问题中高阶最小值的存在性
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-11 DOI: arxiv-2409.07205
Cyrill B. Muratov, Theresa M. Simon, Valeriy V. Slastikov
{"title":"Existence of higher degree minimizers in the magnetic skyrmion problem","authors":"Cyrill B. Muratov, Theresa M. Simon, Valeriy V. Slastikov","doi":"arxiv-2409.07205","DOIUrl":"https://doi.org/arxiv-2409.07205","url":null,"abstract":"We demonstrate existence of topologically nontrivial energy minimizing maps\u0000of a given positive degree from bounded domains in the plane to $mathbb S^2$\u0000in a variational model describing magnetizations in ultrathin ferromagnetic\u0000films with Dzyaloshinskii-Moriya interaction. Our strategy is to insert tiny\u0000truncated Belavin-Polyakov profiles in carefully chosen locations of lower\u0000degree objects such that the total energy increase lies strictly below the\u0000expected Dirichlet energy contribution, ruling out loss of degree in the limits\u0000of minimizing sequences. The argument requires that the domain be either\u0000sufficiently large or sufficiently slender to accommodate a prescribed degree.\u0000We also show that these higher degree minimizers concentrate on point-like\u0000skyrmionic configurations in a suitable parameter regime.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Application of Quantum Graph Theory to Metamaterial Design: Negative Refraction of Acoustic Waveguide Modes 量子图论在超材料设计中的应用：声波导模式的负折射
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-11 DOI: arxiv-2409.07133
T. M. Lawrie, T. A. Starkey, G. Tanner, D. B. Moore, P. Savage, G. J. Chaplain
{"title":"Application of Quantum Graph Theory to Metamaterial Design: Negative Refraction of Acoustic Waveguide Modes","authors":"T. M. Lawrie, T. A. Starkey, G. Tanner, D. B. Moore, P. Savage, G. J. Chaplain","doi":"arxiv-2409.07133","DOIUrl":"https://doi.org/arxiv-2409.07133","url":null,"abstract":"We leverage quantum graph theory to quickly and accurately characterise\u0000acoustic metamaterials comprising networks of interconnected pipes. Anisotropic\u0000bond lengths are incorporated in the model that correspond to space-coiled\u0000acoustic structures to exhibit dispersion spectra reminiscent of hyperbolic\u0000metamaterials. We construct two metasurfaces with embedded graph structure and,\u0000motivated by the graph theory, infer and fine-tune their dispersive properties\u0000to engineer non-resonant negative refraction of acoustic surface waves at their\u0000interface. Agreement between the graph model, full wave simulations, and\u0000experiments bolsters quantum graph theory as a new paradigm for metamaterial\u0000design.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Introduction to Bell's inequality in Quantum Mechanics 量子力学中的贝尔不等式简介
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-11 DOI: arxiv-2409.07597
M. S. Guimaraes, I. Roditi, S. P. Sorella
{"title":"Introduction to Bell's inequality in Quantum Mechanics","authors":"M. S. Guimaraes, I. Roditi, S. P. Sorella","doi":"arxiv-2409.07597","DOIUrl":"https://doi.org/arxiv-2409.07597","url":null,"abstract":"A pedagogical introduction to Bell's inequality in Quantum Mechanics is\u0000presented. Several examples, ranging from spin $1/2$ to coherent and squeezed\u0000states are worked out. The generalization to Mermin's inequalities and to GHZ\u0000states is also outlined.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rescaling transformations and the Grothendieck bound formalism in a single quantum system 单量子系统中的重定标变换和格罗内狄克约束形式主义
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-11 DOI: arxiv-2409.07270
A. Vourdas
{"title":"Rescaling transformations and the Grothendieck bound formalism in a single quantum system","authors":"A. Vourdas","doi":"arxiv-2409.07270","DOIUrl":"https://doi.org/arxiv-2409.07270","url":null,"abstract":"The Grothedieck bound formalism is studied using `rescaling transformations',\u0000in the context of a single quantum system. The rescaling transformations\u0000enlarge the set of unitary transformations (which apply to isolated systems),\u0000with transformations that change not only the phase but also the absolute value\u0000of the wavefunction, and can be linked to irreversible phenomena (e.g., quantum\u0000tunnelling, damping and amplification, etc). A special case of rescaling\u0000transformations are the dequantisation transformations, which map a Hilbert\u0000space formalism into a formalism of scalars. The Grothendieck formalism\u0000considers a `classical' quadratic form ${cal C}(theta)$ which takes values\u0000less than $1$, and the corresponding `quantum' quadratic form ${cal\u0000Q}(theta)$ which takes values greater than $1$, up to the complex Grothendieck\u0000constant $k_G$. It is shown that ${cal Q}(theta)$ can be expressed as the\u0000trace of the product of $theta$ with two rescaling matrices, and ${cal\u0000C}(theta)$ can be expressed as the trace of the product of $theta$ with two\u0000dequantisation matrices. Values of ${cal Q}(theta)$ in the `ultra-quantum'\u0000region $(1,k_G)$ are very important, because this region is classically\u0000forbidden (${cal C}(theta)$ cannot take values in it). An example with ${cal\u0000Q}(theta)in (1,k_G)$ is given, which is related to phenomena where\u0000classically isolated by high potentials regions of space, communicate through\u0000quantum tunnelling. Other examples show that `ultra-quantumness' according to\u0000the Grothendieck formalism (${cal Q}(theta)in (1,k_G)$), is different from\u0000quantumness according to other criteria (like quantum interference or the\u0000uncertainty principle).","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Algebraic classification of the gravitational field in general metric-affine geometries 一般公转仿射几何中引力场的代数分类
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-11 DOI: arxiv-2409.07153
Sebastian Bahamonde, Jorge Gigante Valcarcel, José M. M. Senovilla
{"title":"Algebraic classification of the gravitational field in general metric-affine geometries","authors":"Sebastian Bahamonde, Jorge Gigante Valcarcel, José M. M. Senovilla","doi":"arxiv-2409.07153","DOIUrl":"https://doi.org/arxiv-2409.07153","url":null,"abstract":"We present the algebraic classification of the gravitational field in\u0000four-dimensional general metric-affine geometries, thus extending the current\u0000results of the literature in the particular framework of Weyl-Cartan geometry\u0000by the presence of the traceless nonmetricity tensor. This quantity switches on\u0000four of the eleven fundamental parts of the irreducible representation of the\u0000curvature tensor under the pseudo-orthogonal group, in such a way that three of\u0000them present similar algebraic types as the ones obtained in Weyl-Cartan\u0000geometry, whereas the remaining one includes thirty independent components and\u0000gives rise to a new algebraic classification. The latter is derived by means of\u0000its principal null directions and their levels of alignment, obtaining a total\u0000number of sixteen main algebraic types, which can be split into many subtypes.\u0000As an immediate application, we determine the algebraic types of the broadest\u0000family of static and spherically symmetric black hole solutions with spin,\u0000dilation and shear charges in Metric-Affine Gravity.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Black hole scattering amplitudes via analytic small-frequency expansion and monodromy 通过解析小频扩展和单色性得出的黑洞散射振幅
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-10 DOI: arxiv-2409.06681
Gleb Aminov, Paolo Arnaudo
{"title":"Black hole scattering amplitudes via analytic small-frequency expansion and monodromy","authors":"Gleb Aminov, Paolo Arnaudo","doi":"arxiv-2409.06681","DOIUrl":"https://doi.org/arxiv-2409.06681","url":null,"abstract":"We utilize three complementary approaches to pinpoint the exact form of\u0000scattering amplitudes in Schwarzschild spacetime. First, we solve the\u0000Regge-Wheeler equation perturbatively in the small-frequency regime. We use the\u0000obtained solutions to determine the monodromy in the near-spatial infinity\u0000region, which leads to a specific partial differential equation on the elements\u0000of the scattering matrix. As a result, it can be written in terms of the\u0000elements of the infinitesimal generator of the monodromy transformation and an\u0000integration constant. This constant is further related to the\u0000Nekrasov-Shatashvili free energy through the resummation of infinitely many\u0000instantons. The quasinormal mode frequencies are also studied in the\u0000small-frequency approximation.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Operational Meaning of Total Energy of Isolated Systems in General Relativity 广义相对论中孤立系统总能量的操作意义
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-10 DOI: arxiv-2409.06698
Abhay Ashtekar, Simone Speziale
{"title":"The Operational Meaning of Total Energy of Isolated Systems in General Relativity","authors":"Abhay Ashtekar, Simone Speziale","doi":"arxiv-2409.06698","DOIUrl":"https://doi.org/arxiv-2409.06698","url":null,"abstract":"We present thought experiments to measure the Arnowitt-Deser-Misner and\u0000Bondi-Sachs energy of isolated systems in general relativity. The expression of\u0000the Bondi-Sachs energy used in the protocol is likely to have other\u0000applications. In particular, it is well-suited to to be promoted to an operator\u0000in non-perturbative loop quantum gravity.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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