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Uniqueness of mild solutions to the Navier-Stokes equations in $big(C((0,T];L^d(mathbb{R}^d))cap L^infty((0,T);L^d(mathbb{R}^d))big)^d$ 纳维-斯托克斯方程在 $big(C((0,T];L^d(mathbb{R}^d))cap Linfty((0,T);L^d(mathbb{R}^d))big)^d$ 中的温和解的唯一性
arXiv - PHYS - Mathematical Physics Pub Date : 2024-02-02 DOI: arxiv-2402.01174
Zhirun Zhan
{"title":"Uniqueness of mild solutions to the Navier-Stokes equations in $big(C((0,T];L^d(mathbb{R}^d))cap L^infty((0,T);L^d(mathbb{R}^d))big)^d$","authors":"Zhirun Zhan","doi":"arxiv-2402.01174","DOIUrl":"https://doi.org/arxiv-2402.01174","url":null,"abstract":"This paper deals with the uniqueness of mild solutions to the forced or\u0000unforced Navier-Stokes equations in the whole space. It is known that the\u0000uniqueness of mild solutions to the unforced Navier-Stokes equations holds in\u0000$big(L^{infty}((0,T);L^d(mathbb{R}^d))big)^d$ when $dgeq 4$, and in\u0000$big(C([0,T];L^d(mathbb{R}^d))big)^d$ when $dgeq3$. As for the forced\u0000Navier-Stokes equations, when $dgeq3$ the uniqueness of mild solutions in\u0000$big(C([0,T];L^{d}(mathbb{R}^d))big)^d$ with force $f$ in some Lorentz space\u0000is known. In this paper we show that for $dgeq3$, the uniqueness of mild\u0000solutions to the forced Navier-Stokes equations in\u0000$big(C((0,T];L^d(mathbb{R}^d))cap L^infty((0,T);L^d(mathbb{R}^d))big)^d$\u0000holds when there is a mild solution in $big(C([0,T];L^d(mathbb{R}^d))big)^d$\u0000with the same initial data and force. As a corollary of this result, we\u0000establish the uniqueness of mild solutions to the unforced Navier-Stokes\u0000equations in $big(C((0,T];L^3(mathbb{R}^3))cap\u0000L^infty((0,T);L^3(mathbb{R}^3))big)^3$.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769029","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
Critical Casimir effect in a disordered $O(2)$-symmetric model 无序$O(2)$对称模型中的临界卡西米尔效应
arXiv - PHYS - Mathematical Physics Pub Date : 2024-02-02 DOI: arxiv-2402.01588
G. O. Heymans, N. F. Svaiter, B. F. Svaiter, G. Krein
{"title":"Critical Casimir effect in a disordered $O(2)$-symmetric model","authors":"G. O. Heymans, N. F. Svaiter, B. F. Svaiter, G. Krein","doi":"arxiv-2402.01588","DOIUrl":"https://doi.org/arxiv-2402.01588","url":null,"abstract":"Critical Casimir effect appears when critical fluctuations of an order\u0000parameter interact with classical boundaries. We investigate this effect in the\u0000setting of a Landau-Ginzburg model with continuous symmetry in the presence of\u0000quenched disorder. The quenched free energy is written as an asymptotic series\u0000of moments of the models partition function. Our main result is that, in the\u0000presence of a strong disorder, Goldstone modes of the system contribute either\u0000with an attractive or with a repulsive force. This result was obtained using\u0000the distributional zeta-function method without relying on any particular\u0000ansatz in the functional space of the moments of the partition function.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139768942","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
Twisted TMDs in the small-angle limit: exponentially flat and trivial bands 小角度极限下的扭曲 TMD：指数平坦带和琐碎带
arXiv - PHYS - Mathematical Physics Pub Date : 2024-01-11 DOI: arxiv-2401.06078
Simon Becker, Mengxuan Yang
{"title":"Twisted TMDs in the small-angle limit: exponentially flat and trivial bands","authors":"Simon Becker, Mengxuan Yang","doi":"arxiv-2401.06078","DOIUrl":"https://doi.org/arxiv-2401.06078","url":null,"abstract":"Recent experiments discovered fractional Chern insulator states at zero\u0000magnetic field in twisted bilayer MoTe$_2$ [C23,Z23] and WSe$_2$ [MD23]. In\u0000this article, we study the MacDonald Hamiltonian for twisted transition metal\u0000dichalcogenides (TMDs) and analyze the low-lying spectrum in TMDs in the limit\u0000of small twisting angles. Unlike in twisted bilayer graphene Hamiltonians, we\u0000show that TMDs do not exhibit flat bands. The flatness in TMDs for small\u0000twisting angles is due to spatial confinement by a matrix-valued potential. We\u0000show that by generalizing semiclassical techniques developed by Simon [Si83]\u0000and Helffer-Sj\"ostrand [HS84] to matrix-valued potentials, there exists a wide\u0000range of model parameters such that the low-lying bands are of exponentially\u0000small width in the twisting angle, topologically trivial, and obey a harmonic\u0000oscillator-type spacing with explicit parameters.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463738","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
Dispersionless limit of the B-Toda hierarchy B-Toda 层次结构的无分散极限
arXiv - PHYS - Mathematical Physics Pub Date : 2024-01-11 DOI: arxiv-2401.05919
A. Zabrodin
{"title":"Dispersionless limit of the B-Toda hierarchy","authors":"A. Zabrodin","doi":"arxiv-2401.05919","DOIUrl":"https://doi.org/arxiv-2401.05919","url":null,"abstract":"We study the dispersionless limit of the recently introduced Toda lattice\u0000hierarchy with constraint of type B (the B-Toda hierarchy) and compare it with\u0000that of the DKP and C-Toda hierarchies. The dispersionless limits of the B-Toda\u0000and C-Toda hierarchies turn out to be the same.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463650","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
Integrability and non-invertible symmetries of projector spin chains 投影自旋链的积分性和不可逆转对称性
arXiv - PHYS - Mathematical Physics Pub Date : 2024-01-11 DOI: arxiv-2401.05662
Pramod Padmanabhan, Kun Hao, Vladimir Korepin
{"title":"Integrability and non-invertible symmetries of projector spin chains","authors":"Pramod Padmanabhan, Kun Hao, Vladimir Korepin","doi":"arxiv-2401.05662","DOIUrl":"https://doi.org/arxiv-2401.05662","url":null,"abstract":"We show that nearest-neighbor spin chains composed of projectors to 2-qudit\u0000product states are integrable. The $R$-matrices (with a multidimensional\u0000spectral parameter) include additive as well as non-additive parameters. They\u0000satisfy the colored Yang-Baxter equation. The local terms of the resulting\u0000Hamiltonians exhaust projectors with all possible ranks for a 2-qudit space.\u0000The Hamiltonian can be Hermitian or not, with or without frustration. The\u0000ground state structures of the frustration-free qubit spin chains are analysed.\u0000These systems have either global or local non-invertible symmetries. In\u0000particular, the rank 1 case has two product ground states that break global\u0000non-invertible symmetries (analogous to the case of the two ferromagnetic\u0000states breaking the global $mathbb{Z}_2$ symmetry of the $XXX$ spin chain).\u0000The Bravyi-Gosset conditions for spectral gaps show that these systems are\u0000gapped. The associated Yang-Baxter algebra and the spectrum of the transfer\u0000matrix are also studied.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463861","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
Analytical approximations for generalized quantum Rabi models 广义量子拉比模型的分析近似值
arXiv - PHYS - Mathematical Physics Pub Date : 2024-01-11 DOI: arxiv-2401.05615
Chon-Fai Kam, Yang Chen
{"title":"Analytical approximations for generalized quantum Rabi models","authors":"Chon-Fai Kam, Yang Chen","doi":"arxiv-2401.05615","DOIUrl":"https://doi.org/arxiv-2401.05615","url":null,"abstract":"The quantum Rabi model is essential for understanding interacting quantum\u0000systems. It serves as the simplest non-integrable yet solvable model describing\u0000the interaction between a two-level system and a single mode of a bosonic\u0000field. In this study, we delve into the exploration of the generalized quantum\u0000Rabi model, wherein the bosonic mode of the field undergoes squeezing.\u0000Utilizing the Segal-Bargmann representation of the infinite-dimensional Hilbert\u0000space, we demonstrate that the energy spectrum of the generalized quantum Rabi\u0000model, when both the Rabi coupling strength and the squeezing strength are not\u0000significantly large compared to the field mode frequency, can be analytically\u0000determined by a bi-confluent Fuchsian equation with two regular singularities\u0000at 0 and 1 and an irregular singularity of rank two at infinity.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463781","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
Lagrangian Relations and Quantum $L_infty$ Algebras 拉格朗日关系与量子 $L_infty$ 算法
arXiv - PHYS - Mathematical Physics Pub Date : 2024-01-11 DOI: arxiv-2401.06110
Branislav Jurčo, Ján Pulmann, Martin Zika
{"title":"Lagrangian Relations and Quantum $L_infty$ Algebras","authors":"Branislav Jurčo, Ján Pulmann, Martin Zika","doi":"arxiv-2401.06110","DOIUrl":"https://doi.org/arxiv-2401.06110","url":null,"abstract":"Quantum $L_infty$ algebras are higher loop generalizations of cyclic\u0000$L_infty$ algebras. Motivated by the problem of defining morphisms between\u0000such algebras, we construct a linear category of $(-1)$-shifted symplectic\u0000vector spaces and distributional half-densities, originally proposed by\u0000v{S}evera. Morphisms in this category can be given both by formal\u0000half-densities and Lagrangian relations; we prove that the composition of such\u0000morphisms recovers the construction of homotopy transfer of quantum $L_infty$\u0000algebras. Finally, using this category, we propose a new notion of a relation\u0000between quantum $L_infty$ algebras.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139458769","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
Classical and Quantum solutions in Scalar field cosmology via the Eisenhart lift and linearization 通过艾森哈特提升和线性化实现标量场宇宙学中的经典和量子解
arXiv - PHYS - Mathematical Physics Pub Date : 2024-01-11 DOI: arxiv-2401.05775
Andronikos Paliathanasis
{"title":"Classical and Quantum solutions in Scalar field cosmology via the Eisenhart lift and linearization","authors":"Andronikos Paliathanasis","doi":"arxiv-2401.05775","DOIUrl":"https://doi.org/arxiv-2401.05775","url":null,"abstract":"This study introduces a novel approach for solving the cosmological field\u0000equations within scalar field theory by employing the Eisenhart lift. The field\u0000equations are reformulated as a system of geodesic equations for the Eisenhart\u0000metric. In the case of an exponential potential, the Eisenhart metric is shown\u0000to be conformally flat. By applying basic geometric principles, a new set of\u0000dynamical variables is identified, allowing for the linearization of the field\u0000equations and the derivation of classical cosmological solutions. However, the\u0000quantization of the Eisenhart system reveals a distinct set of solutions for\u0000the wavefunction, particularly in the presence of symmetry breaking at the\u0000quantum level.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463784","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
Invariance principle for the KPZ equation arising in stochastic flows of kernels 核随机流中出现的 KPZ 方程的不变性原理
arXiv - PHYS - Mathematical Physics Pub Date : 2024-01-11 DOI: arxiv-2401.06073
Shalin Parekh
{"title":"Invariance principle for the KPZ equation arising in stochastic flows of kernels","authors":"Shalin Parekh","doi":"arxiv-2401.06073","DOIUrl":"https://doi.org/arxiv-2401.06073","url":null,"abstract":"We consider a generalized model of random walk in dynamical random\u0000environment, and we show that the multiplicative-noise stochastic heat equation\u0000(SHE) describes the fluctuations of the quenched density at a certain precise\u0000location in the tail. The distribution of transition kernels is fixed rather\u0000than changing under the diffusive rescaling of space-time, i.e., there is no\u0000critical tuning of the model parameters when scaling to the stochastic PDE\u0000limit. The proof is done by pushing the methods developed in [arxiv 2304.14279,\u0000arXiv 2311.09151] to their maximum, substantially weakening the assumptions and\u0000obtaining fairly sharp conditions under which one expects to see the SHE arise\u0000in a wide variety of random walk models in random media. In particular we are\u0000able to get rid of conditions such as nearest-neighbor interaction as well as\u0000spatial independence of quenched transition kernels. Moreover, we observe an\u0000entire hierarchy of moderate deviation exponents at which the SHE can be found,\u0000confirming a physics prediction of J. Hass.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463823","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
Enhanced Stability in Quantum Optimal Transport Pseudometrics: From Hartree to Vlasov-Poisson 量子优化传输伪计量学中的增强稳定性：从哈特里到弗拉索夫-泊松
arXiv - PHYS - Mathematical Physics Pub Date : 2024-01-11 DOI: arxiv-2401.05773
Mikaela Iacobelli, Laurent Lafleche
{"title":"Enhanced Stability in Quantum Optimal Transport Pseudometrics: From Hartree to Vlasov-Poisson","authors":"Mikaela Iacobelli, Laurent Lafleche","doi":"arxiv-2401.05773","DOIUrl":"https://doi.org/arxiv-2401.05773","url":null,"abstract":"In this paper we establish almost-optimal stability estimates in quantum\u0000optimal transport pseudometrics for the semiclassical limit of the Hartree\u0000dynamics to the Vlasov-Poisson equation, in the regime where the solutions have\u0000bounded densities. We combine Golse and Paul's method from [Arch. Ration. Mech.\u0000Anal. 223:57-94, 2017], which uses a semiclassical version of the optimal\u0000transport distance and which was adapted to the case of the Coulomb and\u0000gravitational interactions by the second author in [J. Stat. Phys. 177:20-60,\u00002019], with a new approach developed by the first author in [Arch. Ration.\u0000Mech. Anal. 244:27-50, 2022] to quantitatively improve stability estimates in\u0000kinetic theory.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463618","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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