arXiv - PHYS - Mathematical Physics最新文献_第8页

Glassy word problems: ultraslow relaxation, Hilbert space jamming, and computational complexity 玻璃文字问题：超慢速松弛、希尔伯特空间干扰和计算复杂性

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-07 DOI: arxiv-2312.04562

Shankar Balasubramanian, Sarang Gopalakrishnan, Alexey Khudorozhkov, Ethan Lake

{"title":"Glassy word problems: ultraslow relaxation, Hilbert space jamming, and computational complexity","authors":"Shankar Balasubramanian, Sarang Gopalakrishnan, Alexey Khudorozhkov, Ethan Lake","doi":"arxiv-2312.04562","DOIUrl":"https://doi.org/arxiv-2312.04562","url":null,"abstract":"We introduce a family of local models of dynamics based on ``word problems''\u0000from computer science and group theory, for which we can place rigorous lower\u0000bounds on relaxation timescales. These models can be regarded either as random\u0000circuit or local Hamiltonian dynamics, and include many familiar examples of\u0000constrained dynamics as special cases. The configuration space of these models\u0000splits into dynamically disconnected sectors, and for initial states to relax,\u0000they must ``work out'' the other states in the sector to which they belong.\u0000When this problem has a high time complexity, relaxation is slow. In some of\u0000the cases we study, this problem also has high space complexity. When the space\u0000complexity is larger than the system size, an unconventional type of jamming\u0000transition can occur, whereby a system of a fixed size is not ergodic, but can\u0000be made ergodic by appending a large reservoir of sites in a trivial product\u0000state. This manifests itself in a new type of Hilbert space fragmentation that\u0000we call fragile fragmentation. We present explicit examples where slow\u0000relaxation and jamming strongly modify the hydrodynamics of conserved\u0000densities. In one example, density modulations of wavevector $q$ exhibit almost\u0000no relaxation until times $O(exp(1/q))$, at which point they abruptly\u0000collapse. We also comment on extensions of our results to higher dimensions.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138555542","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

Stability of buoyant-Couette flow in a vertical porous slot 垂直多孔槽中浮力-库埃特流动的稳定性

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-07 DOI: arxiv-2312.04270

B. M. Shankar, I. S. Shivakumara

{"title":"Stability of buoyant-Couette flow in a vertical porous slot","authors":"B. M. Shankar, I. S. Shivakumara","doi":"arxiv-2312.04270","DOIUrl":"https://doi.org/arxiv-2312.04270","url":null,"abstract":"The stability of two-dimensional buoyancy-driven convection in a vertical\u0000porous slot, wherein a plane Couette flow is additionally present, is studied.\u0000This complex fluid flow scenario is examined under the influence of Robin-type\u0000boundary conditions, which are applied to perturbations in both velocity and\u0000temperature. The inclusion of a time-derivative velocity term within the Darcy\u0000momentum equation notably introduces intricacies to the study. The stability of\u0000the basic natural convection flow is primarily governed by several key\u0000parameters namely, the P'eclet number, the Prandtl-Darcy number, the Biot\u0000number and a non-negative parameter that dictates the nature of the vertical\u0000boundaries. Through numerical analysis, the stability eigenvalue problem is\u0000solved for a variety of combinations of boundary conditions. The outcomes of\u0000this analysis reveal the critical threshold values that signify the onset of\u0000instability. Furthermore, a detailed examination of the stability of the system\u0000has provided insights into both its commonalities and distinctions under\u0000different conditions. It is observed that, except for the scenario featuring\u0000impermeable-isothermal boundaries, the underlying base flow exhibits\u0000instability when subjected to various other configurations of perturbed\u0000velocity and temperature boundary conditions. This underscores the notion that\u0000the presence of Couette flow alone does not suffice to induce instability\u0000within the system. The plots depicting neutral stability curves show either\u0000bi-modal or uni-modal characteristics, contingent upon specific parameter\u0000values that influence the onset of instability.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138555272","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

Affine Symmetries for ABJM Partition Function and its Generalization ABJM 平分函数的仿射对称性及其泛化

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-07 DOI: arxiv-2312.04206

Sanefumi Moriyama, Tomoki Nosaka

引用次数: 0

Ergodic theorems for continuous-time quantum walks on crystal lattices and the torus 晶格和环上连续时间量子行走的遍历定理

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-07 DOI: arxiv-2312.04492

Anne Boutet de Monvel, Mostafa Sabri

引用次数: 0

Para-spaces, their differential analysis and an application to Green's quantisation 准空间、其微分分析以及在格林量子化中的应用

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-07 DOI: arxiv-2312.04250

Ruibin Zhang

引用次数: 0

Zero-Class Poisson for Rare-Event Studies 零类泊松用于罕见事件研究

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-06 DOI: arxiv-2312.03894

Thomas M. Semkow

引用次数: 0

On the Obtaining Solutions of Nonlinear Differential Equations by Means of the Solutions of Simpler Linear or Nonlinear Differential Equations 论通过较简单线性或非线性微分方程的解来获取非线性微分方程的解

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-06 DOI: arxiv-2312.03621

Nikolay K. Vitanov

{"title":"On the Obtaining Solutions of Nonlinear Differential Equations by Means of the Solutions of Simpler Linear or Nonlinear Differential Equations","authors":"Nikolay K. Vitanov","doi":"arxiv-2312.03621","DOIUrl":"https://doi.org/arxiv-2312.03621","url":null,"abstract":"In this article, we follow an idea that is opposite to the idea of Hopf and\u0000Cole: we use transformations in order to transform simpler linear or nonlinear\u0000differential equations (with known solutions) to more complicated nonlinear\u0000differential equations. In such a way, we can obtain numerous exact solutions\u0000of nonlinear differential equations. We apply this methodology to the classical\u0000parabolic differential equation (the wave equation), to the classical\u0000hyperbolic differential equation (the heat equation), and to the classical\u0000elliptic differential equation (Laplace equation). In addition, we use the\u0000methodology to obtain exact solutions of nonlinear ordinary differential\u0000equations by means of the solutions of linear differential equations and by\u0000means of the solutions of the nonlinear differential equations of Bernoulli and\u0000Riccati. Finally, we demonstrate the capacity of the methodology to lead to\u0000exact solutions of nonlinear partial differential equations on the basis of\u0000known solutions of other nonlinear partial differential equations. As an\u0000example of this, we use the Korteweg--de Vries equation and its solutions.\u0000Traveling wave solutions of nonlinear differential equations are of special\u0000interest in this article. We demonstrate the existence of the following\u0000phenomena described by some of the obtained solutions: (i) occurrence of the\u0000solitary wave--solitary antiwave from the solution, which is zero at the\u0000initial moment (analogy of an occurrence of particle and antiparticle from the\u0000vacuum); (ii) splitting of a nonlinear solitary wave into two solitary waves\u0000(analogy of splitting of a particle into two particles); (iii) soliton behavior\u0000of some of the obtained waves; (iv) existence of solitons which move with the\u0000same velocity despite the different shape and amplitude of the solitons.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138545963","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

Temporal coupled-mode theory in nonlinear resonant photonics: From basic principles to contemporary systems with 2D materials, dispersion, loss, and gain 非线性谐振光子学中的时间耦合模式理论：从基本原理到二维材料、色散、损耗和增益的现代系统

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-06 DOI: arxiv-2312.03539

Thomas Christopoulos, Odysseas Tsilipakos, Emmanouil E. Kriezis

{"title":"Temporal coupled-mode theory in nonlinear resonant photonics: From basic principles to contemporary systems with 2D materials, dispersion, loss, and gain","authors":"Thomas Christopoulos, Odysseas Tsilipakos, Emmanouil E. Kriezis","doi":"arxiv-2312.03539","DOIUrl":"https://doi.org/arxiv-2312.03539","url":null,"abstract":"Temporal coupled-mode theory (CMT) is an acclaimed and widely used\u0000theoretical framework for modeling the continuous wave (CW) response and\u0000temporal dynamics of any integrated or free-space photonic resonant structure.\u0000It was initially employed to understand how energy is coupled into and out of a\u0000cavity and how it is exchanged between different resonant modes. In the 30\u0000years that followed its establishment, CMT has been expanded to describe a\u0000broad range of nonlinear interactions as well (self- and cross-phase\u0000modulation, saturable absorption, frequency generation, gain, etc.). In this\u0000tutorial, we thoroughly present the basic principles and the evolution of CMT\u0000throughout the years, showcasing its immense capabilities for the analysis and\u0000design of linear and nonlinear resonant photonic systems. Importantly, we focus\u0000on examples of modern, open nanophotonic resonators incorporating contemporary\u0000bulk or sheet (2D) materials that may be lossy and dispersive. For each\u0000linear/nonlinear effect under study we follow a meticulous, step-by-step\u0000approach, starting from an accurate model of the physical phenomenon and\u0000proceeding to its introduction in the CMT framework all the way to the\u0000efficient solution of the resulting system of equations. Our work highlights\u0000the merits of CMT as an efficient, accurate, and versatile theoretical tool. We\u0000envision that it can serve both as an introductory reference for any reader, as\u0000well as a comprehensive handbook on how to incorporate a broad range of linear\u0000and nonlinear effects in the CMT framework.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138545962","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

Vertex algebras from divisors on Calabi-Yau threefolds 来自 Calabi-Yau 三折上除数的顶点代数

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-06 DOI: arxiv-2312.03648

Dylan Butson

{"title":"Vertex algebras from divisors on Calabi-Yau threefolds","authors":"Dylan Butson","doi":"arxiv-2312.03648","DOIUrl":"https://doi.org/arxiv-2312.03648","url":null,"abstract":"We construct vertex algebras $mathbb{V}(Y,S)$ from divisors $S$ on toric\u0000Calabi-Yau threefolds $Y$, satisfying conjectures of Gaiotto-Rapcak and\u0000Feigin-Gukov, as the kernel of screening operators on lattice vertex algebras\u0000determined by the GKM graph of $Y$ and a filtration on $mathcal{O}_S$. We\u0000prove that there are representations of $mathbb{V}(Y,S)$ on the homology\u0000groups of various moduli spaces of coherent sheaves on $Y$ supported on $S$\u0000constructed in a companion paper with Rapcak, defined by certain Hecke\u0000modifications of these sheaves along points and curve classes in the divisor\u0000$S$. This generalizes the common mathematical formulation of a conjecture of\u0000Alday-Gaiotto-Tachikawa, the special case in which $Y=mathbb{C}^3$ and\u0000$S=r[mathbb{C}^2]$, to toric threefolds and divisors as proposed by\u0000Gaiotto-Rapcak. We outline an approach to the general conjecture and prove many\u0000special cases and partial results using tools developed in the companion paper,\u0000following the proof of the original conjecture by Schiffmann-Vasserot and its\u0000generalization to divisors in $mathbb{C}^3$ by Rapcak-Soibelman-Yang-Zhao. The vertex algebras $mathbb{V}(Y,S)$ conjecturally include $W$-superalgebras\u0000$ W_{f_0,f_1}^kappa(mathfrak{gl}_{m|n})$ and genus zero class $mathcal{S}$\u0000chiral algebras $mathbb{V}^{mathcal{S}}_{text{Gl}_m;f_1,...,f_k}$, each for\u0000general nilpotents $f_i$. By definition, this implies the existence of a family\u0000of compatible free field realizations of these vertex algebras, relevant to\u0000their parabolic induction and inverse quantum Hamiltonian reduction. We prove\u0000these conjectures in the examples of lowest non-trivial rank for each case, and\u0000outline the proof in general for some cases.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138545814","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 three limits of the hydrostatic approximation 流体静力学近似的三个极限

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-06 DOI: arxiv-2312.03418

Ken Furukawa, Yoshikazu Giga, Matthias Hieber, Amru Hussein, Takahito Kashiwabara, Marc Wrona

{"title":"The three limits of the hydrostatic approximation","authors":"Ken Furukawa, Yoshikazu Giga, Matthias Hieber, Amru Hussein, Takahito Kashiwabara, Marc Wrona","doi":"arxiv-2312.03418","DOIUrl":"https://doi.org/arxiv-2312.03418","url":null,"abstract":"The primitive equations are derived from the $3D$-Navier-Stokes equations by\u0000the hydrostatic approximation. Formally, assuming an $varepsilon$-thin domain\u0000and anisotropic viscosities with vertical viscosity\u0000$nu_z=mathcal{O}(varepsilon^gamma)$ where $gamma=2$, one obtains the\u0000primitive equations with full viscosity as $varepsilonto 0$. Here, we take\u0000two more limit equations into consideration: For $gamma<2$ the\u0000$2D$-Navier-Stokes equations are obtained. For $gamma>2$ the primitive\u0000equations with only horizontal viscosity $-Delta_H$ as $varepsilonto 0$.\u0000Thus, there are three possible limits of the hydrostatic approximation\u0000depending on the assumption on the vertical viscosity. The latter convergence\u0000has been proven recently by Li, Titi, and Yuan using energy estimates. Here, we\u0000consider more generally $nu_z=varepsilon^2 delta$ and show how maximal\u0000regularity methods and quadratic inequalities can be an efficient approach to\u0000the same end for $varepsilon,deltato 0$. The flexibility of our methods is\u0000also illustrated by the convergence for $deltato infty$ and $varepsilonto\u00000$ to the $2D$-Navier-Stokes equations.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138545906","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