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General relaxation model for a homogeneous plasma with spherically symmetric velocity space 具有球形对称速度空间的均质等离子体的一般弛豫模型
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-16 DOI: arxiv-2409.10060
Yanpeng Wang, Shichao Wu, Peifeng Fan
{"title":"General relaxation model for a homogeneous plasma with spherically symmetric velocity space","authors":"Yanpeng Wang, Shichao Wu, Peifeng Fan","doi":"arxiv-2409.10060","DOIUrl":"https://doi.org/arxiv-2409.10060","url":null,"abstract":"A kinetic moment-closed model, derived from the Vlasov-Fokker-Planck equation\u0000for homogeneous plasma with spherically symmetric velocity space, is introduced\u0000as a general relaxation model. The closed form of this nonlinear model is\u0000presented by introducing a set new functions called R function and R\u0000integration. This model, based on the finitely distinguishable independent\u0000features hypothesis, allows for capturing the nature of equilibrium state. From\u0000this relaxation model, a general temperature relaxation model is derived and\u0000the general characteristic frequency of temperature relaxation when velocity\u0000space exhibits spherical symmetry is presented.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260470","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
Acoustic Lattice Resonances and Generalised Rayleigh--Bloch Waves 声晶格共振和广义瑞利-布洛赫波
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-16 DOI: arxiv-2409.10074
G. J. Chaplain, S. C. Hawkins, M. A. Peter, L. G. Bennetts, T. A. Starkey
{"title":"Acoustic Lattice Resonances and Generalised Rayleigh--Bloch Waves","authors":"G. J. Chaplain, S. C. Hawkins, M. A. Peter, L. G. Bennetts, T. A. Starkey","doi":"arxiv-2409.10074","DOIUrl":"https://doi.org/arxiv-2409.10074","url":null,"abstract":"The intrigue of waves on periodic lattices and gratings has resonated with\u0000physicists and mathematicians alike for decades. In-depth analysis has been\u0000devoted to the seemingly simplest array system: a one-dimensionally periodic\u0000lattice of two-dimensional scatterers embedded in a dispersionless medium\u0000governed by the Helmholtz equation. We investigate such a system and\u0000experimentally confirm the existence of a new class of generalised\u0000Rayleigh--Bloch waves that have been recently theorised to exist in classical\u0000wave regimes, without the need for resonant scatterers. Airborne acoustics\u0000serves as such a regime and here we experimentally observe the first\u0000generalised Rayleigh--Bloch waves above the first cut-off, i.e., in the\u0000radiative regime. We consider radiative acoustic lattice resonances along a\u0000diffraction grating and connect them to generalised Rayleigh--Bloch waves by\u0000considering both short and long arrays of non-resonant 2D cylindrical Neumann\u0000scatterers embedded in air. On short arrays, we observe finite lattice\u0000resonances under continuous wave excitation, and on long arrays, we observe\u0000propagating Rayleigh--Bloch waves under pulsed excitation. We interpret their\u0000existence by considering multiple wave scattering theory and, in doing so,\u0000unify differing nomenclatures used to describe waves on infinite periodic and\u0000finite arrays and the interpretation of their dispersive properties.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260469","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
$mathrm{U}(1)^{n}$ Chern-Simons theory: partition function, reciprocity formula and CS-duality $mathrm{U}(1)^{n}$ 切尔-西蒙斯理论：分割函数、互易公式和 CS-二重性
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-16 DOI: arxiv-2409.10734
Han-Miru Kim, Philippe Mathieu, Michail Tagaris, Frank Thuillier
{"title":"$mathrm{U}(1)^{n}$ Chern-Simons theory: partition function, reciprocity formula and CS-duality","authors":"Han-Miru Kim, Philippe Mathieu, Michail Tagaris, Frank Thuillier","doi":"arxiv-2409.10734","DOIUrl":"https://doi.org/arxiv-2409.10734","url":null,"abstract":"The $mathrm{U}(1)$ Chern-Simons theory can be extended to a topological\u0000$mathrm{U}(1)^n$ theory by taking a combination of Chern-Simons and BF\u0000actions, the mixing being achieved with the help of a collection of integer\u0000coupling constants. Based on the Deligne-Beilinson cohomology, a partition\u0000function can then be computed for such a $mathrm{U}(1)^n$ Chern-Simons theory.\u0000This partition function is clearly a topological invariant of the closed\u0000oriented $3$-manifold on which the theory is defined. Then, by applying a\u0000reciprocity formula a new expression of this invariant is obtained which should\u0000be a Reshetikhin-Turaev invariant. Finally, a duality between $mathrm{U}(1)^n$\u0000Chern-Simons theories is demonstrated.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"83 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260399","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 full electroweak interaction: an autonomous account 完整的电弱相互作用：自主的解释
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-16 DOI: arxiv-2409.10668
José M. Gracia-Bondía, Karl-Henning Rehren, Joseph C. Várilly
{"title":"The full electroweak interaction: an autonomous account","authors":"José M. Gracia-Bondía, Karl-Henning Rehren, Joseph C. Várilly","doi":"arxiv-2409.10668","DOIUrl":"https://doi.org/arxiv-2409.10668","url":null,"abstract":"The precise renormalizable interactions in the bosonic sector of electroweak\u0000theory are intrinsically determined in the autonomous approach to perturbation\u0000theory. This proceeds directly on the Hilbert-Fock space built on the Wigner\u0000unirreps of the physical particles, with their given masses: those of three\u0000massive vector bosons, a photon, and a massive scalar (the \"higgs\"). Neither\u0000\"gauge choices\" nor an unobservable \"mechanism of spontaneous symmetry\u0000breaking\" are invoked. Instead, to proceed on Hilbert space requires using\u0000string-localized fields to describe the vector bosons. In such a framework, the\u0000condition of string independence of the S-matrix yields consistency constraints\u0000on the coupling coefficients, the unique outcome being the experimentally known\u0000one. The analysis can be largely carried out for other configurations of\u0000massive and massless vector bosons, paving the way towards consideration of\u0000consistent mass patterns beyond those of the electroweak theory.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"207 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260456","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
Symmetries of Liouvillians of squeeze-driven parametric oscillators 挤压驱动参数振荡器的刘维利对称性
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-16 DOI: arxiv-2409.10744
Francesco Iachello, Colin V. Coane, Jayameenakshi Venkatraman
{"title":"Symmetries of Liouvillians of squeeze-driven parametric oscillators","authors":"Francesco Iachello, Colin V. Coane, Jayameenakshi Venkatraman","doi":"arxiv-2409.10744","DOIUrl":"https://doi.org/arxiv-2409.10744","url":null,"abstract":"We study the symmetries of the Liouville superoperator of one dimensional\u0000parametric oscillators, especially the so-called squeeze-driven Kerr\u0000oscillator, and discover a remarkable quasi-spin symmetry $su(2)$ at integer\u0000values of the ratio $eta =omega /K$ of the detuning parameter $omega$ to the\u0000Kerr coefficient $K$, which reflects the symmetry previously found for the\u0000Hamiltonian operator. We find that the Liouvillian of an $su(2)$ representation\u0000$leftvert j,m_{j}rightrangle$ has a characteristic double-ellipsoidal\u0000structure, and calculate the relaxation time $T_{X}$ for this structure. We\u0000then study the phase transitions of the Liouvillian which occur as a function\u0000of the parameters $xi =varepsilon _{2}/K$ and $eta=omega /K$. Finally, we\u0000study the temperature dependence of the spectrum of eigenvalues of the\u0000Liouvillian. Our findings may have applications in the generation and\u0000stabilization of states of interest in quantum computing.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260455","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
An explicit tensor notation for quantum computing 量子计算的显式张量符号
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-16 DOI: arxiv-2409.10487
Valentina Amitrano, Francesco Pederiva
{"title":"An explicit tensor notation for quantum computing","authors":"Valentina Amitrano, Francesco Pederiva","doi":"arxiv-2409.10487","DOIUrl":"https://doi.org/arxiv-2409.10487","url":null,"abstract":"This paper introduces a formalism that aims to describe the intricacies of\u0000quantum computation by establishing a connection with the mathematical\u0000foundations of tensor theory and multilinear maps. The focus is on providing a\u0000comprehensive representation of quantum states for multiple qubits and the\u0000quantum gates that manipulate them. The proposed formalism could contribute to\u0000a more intuitive representation of qubit states, and to a clear visualisation\u0000of the entanglement property. The main advantages of this formalism are that it\u0000preserves the fundamental structure of the Hilbert space to which quantum\u0000states belong, and also reduces the computational cost associated with\u0000classical prediction of the effect of quantum gates on multi-qubit states. A\u0000connection between the ability to generate entanglement and the quantum gate\u0000representation is also established.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260465","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 Weakly Nonlinear Schrödinger Equation in Higher Dimensions with Quasi-periodic Initial Data 具有准周期初始数据的高维度弱非线性薛定谔方程
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-16 DOI: arxiv-2409.10006
Fei XuJilin University
{"title":"The Weakly Nonlinear Schrödinger Equation in Higher Dimensions with Quasi-periodic Initial Data","authors":"Fei XuJilin University","doi":"arxiv-2409.10006","DOIUrl":"https://doi.org/arxiv-2409.10006","url":null,"abstract":"In this paper, under the exponential/polynomial decay condition in Fourier\u0000space, we prove that the nonlinear solution to the quasi-periodic Cauchy\u0000problem for the weakly nonlinear Schr\"odinger equation in higher dimensions\u0000will asymptotically approach the associated linear solution within a specific\u0000time scale. The proof is based on a combinatorial analysis method. Our results\u0000and methods work for {em arbitrary} space dimensions and focusing/defocusing\u0000{em arbitrary} power-law nonlinearities.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260471","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 thermodynamic limit in mean field neural networks 平均场神经网络的热力学极限
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-16 DOI: arxiv-2409.10145
Elena Agliari, Adriano Barra, Pierluigi Bianco, Alberto Fachechi, Diego Pallara
{"title":"The thermodynamic limit in mean field neural networks","authors":"Elena Agliari, Adriano Barra, Pierluigi Bianco, Alberto Fachechi, Diego Pallara","doi":"arxiv-2409.10145","DOIUrl":"https://doi.org/arxiv-2409.10145","url":null,"abstract":"In the last five decades, mean-field neural-networks have played a crucial\u0000role in modelling associative memories and, in particular, the Hopfield model\u0000has been extensively studied using tools borrowed from the statistical\u0000mechanics of spin glasses. However, achieving mathematical control of the\u0000infinite-volume limit of the model's free-energy has remained elusive, as the\u0000standard treatments developed for spin-glasses have proven unfeasible. Here we\u0000address this long-standing problem by proving that a measure-concentration\u0000assumption for the order parameters of the theory is sufficient for the\u0000existence of the asymptotic limit of the model's free energy. The proof\u0000leverages the equivalence between the free energy of the Hopfield model and a\u0000linear combination of the free energies of a hard and a soft spin-glass, whose\u0000thermodynamic limits are rigorously known. Our work focuses on the\u0000replica-symmetry level of description (for which we recover the explicit\u0000expression of the free-energy found in the eighties via heuristic methods),\u0000yet, our scheme is expected to work also under (at least) the first step of\u0000replica symmetry breaking.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260466","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
Two transitions in complex eigenvalue statistics: Hermiticity and integrability breaking 复特征值统计中的两种转变：隐含性和可整性打破
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-16 DOI: arxiv-2409.10625
G. Akemann, F. Balducci, A. Chenu, P. Päßler, F. Roccati, R. Shir
{"title":"Two transitions in complex eigenvalue statistics: Hermiticity and integrability breaking","authors":"G. Akemann, F. Balducci, A. Chenu, P. Päßler, F. Roccati, R. Shir","doi":"arxiv-2409.10625","DOIUrl":"https://doi.org/arxiv-2409.10625","url":null,"abstract":"Open quantum systems have complex energy eigenvalues which are expected to\u0000follow non-Hermitian random matrix statistics when chaotic, or 2-dimensional\u0000(2d) Poisson statistics when integrable. We investigate the spectral properties\u0000of a many-body quantum spin chain, the Hermitian XXZ Heisenberg model with\u0000imaginary disorder. Its rich complex eigenvalue statistics is found to\u0000separately break both Hermiticity and integrability at different scales of the\u0000disorder strength. With no disorder, the system is integrable and Hermitian,\u0000with spectral statistics corresponding to 1d Poisson. At very small disorder,\u0000we find a transition from 1d Poisson statistics to an effective $D$-dimensional\u0000Poisson point process, showing Hermiticity breaking. At intermediate disorder\u0000we find integrability breaking, and the statistics agrees with that of\u0000non-Hermitian complex symmetric random matrices in class AI$^dag$. For large\u0000disorder, we recover the expected 2d Poisson statistics. Our analysis uses\u0000numerically generated nearest and next-to-nearest neighbour spacing\u0000distributions of an effective 2d Coulomb gas description at inverse temperature\u0000$beta$, fitting them to the spin chain data. We confirm such an effective\u0000description of random matrices in class AI$^dag$ and AII$^dag$ up to\u0000next-to-nearest neighbour spacings.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260458","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
Convergence of integrals on the moduli spaces of curves and cographical matroids 曲线模空间上积分的收敛性和自传体矩阵
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-16 DOI: arxiv-2409.10005
Alexander Polishchuk, Nicholas Proudfoot
{"title":"Convergence of integrals on the moduli spaces of curves and cographical matroids","authors":"Alexander Polishchuk, Nicholas Proudfoot","doi":"arxiv-2409.10005","DOIUrl":"https://doi.org/arxiv-2409.10005","url":null,"abstract":"We determine the convergence regions of certain local integrals on the moduli\u0000spaces of curves in neighborhoods of fixed stable curves in terms of the\u0000combinatorics of the corresponding graphs.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"86 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260472","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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