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Feynman checkers: lattice quantum field theory with real time 费曼跳棋：实时网格量子场论
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-04-09 DOI: 10.1007/s13324-024-00896-0
M. Skopenkov, A. Ustinov
{"title":"Feynman checkers: lattice quantum field theory with real time","authors":"M. Skopenkov,&nbsp;A. Ustinov","doi":"10.1007/s13324-024-00896-0","DOIUrl":"10.1007/s13324-024-00896-0","url":null,"abstract":"<div><p>We present a new completely elementary model that describes the creation, annihilation, and motion of non-interacting electrons and positrons along a line. It is a modification of the model known under the names Feynman checkers or one-dimensional quantum walk. It can be viewed as a six-vertex model with certain complex weights of the vertices. The discrete model is consistent with the continuum quantum field theory, namely, reproduces the known expected charge density as the lattice step tends to zero. It is exactly solvable in terms of hypergeometric functions. We introduce interaction resembling Fermi’s theory and establish perturbation expansion.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140600579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bilinear sparse domination for oscillatory integral operators 振荡积分算子的双线性稀疏支配
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-04-04 DOI: 10.1007/s13324-024-00895-1
Tobias Mattsson
{"title":"Bilinear sparse domination for oscillatory integral operators","authors":"Tobias Mattsson","doi":"10.1007/s13324-024-00895-1","DOIUrl":"10.1007/s13324-024-00895-1","url":null,"abstract":"<div><p>In this paper, we prove bilinear sparse domination bounds for a wide class of Fourier integral operators of general rank, as well as oscillatory integral operators associated to Hörmander symbol classes <span>(S^m_{rho ,delta })</span> for all <span>(0le rho le 1)</span> and <span>(0le delta &lt; 1)</span>, a notable example is the Schrödinger operator. As a consequence, one obtains weak (1, 1) estimates, vector-valued estimates, and a wide range of weighted norm inequalities for these classes of operators.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00895-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140600379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Isometries of absolutely continuous function spaces with respect to the sum-norm 绝对连续函数空间关于和规范的等距性
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-03-26 DOI: 10.1007/s13324-024-00894-2
Maliheh Hosseini, Juan J. Font
{"title":"Isometries of absolutely continuous function spaces with respect to the sum-norm","authors":"Maliheh Hosseini,&nbsp;Juan J. Font","doi":"10.1007/s13324-024-00894-2","DOIUrl":"10.1007/s13324-024-00894-2","url":null,"abstract":"<div><p>In this paper we give a complete description of surjective linear isometries between Banach spaces of absolutely continuous functions on arbitrary (not necessarily compact) subsets of the real line with respect to the sum-norm. We also use this description to study approximate local isometries and approximate 2-local isometries on these spaces. In particular, we present generalizations of all known results concerning such isometries, and obtain the reflexivity and 2-reflexivity of the isometry group of absolutely continuous function spaces in a noncompact framework.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hermite-Hadamard type inequalities for new conditions on h-convex functions via (psi )-Hilfer integral operators 通过 $$psi $$ -Hilfer 积分算子对 h-凸函数新条件的 Hermite-Hadamard 型不等式
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-03-26 DOI: 10.1007/s13324-024-00893-3
Bouharket Benaissa, Noureddine Azzouz, Hüseyin Budak
{"title":"Hermite-Hadamard type inequalities for new conditions on h-convex functions via (psi )-Hilfer integral operators","authors":"Bouharket Benaissa,&nbsp;Noureddine Azzouz,&nbsp;Hüseyin Budak","doi":"10.1007/s13324-024-00893-3","DOIUrl":"10.1007/s13324-024-00893-3","url":null,"abstract":"<div><p>We employ a new function class called <i>B</i>-function to create a new version of fractional Hermite–Hadamard and trapezoid type inequalities on the right-hand side that involves <i>h</i>-convex and <span>(psi )</span>-Hilfer operators. We also provide new midpoint-type inequalities using <i>h</i>-convex functions.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00893-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140300128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rolling reductive homogeneous spaces 滚动还原同质空间
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-03-26 DOI: 10.1007/s13324-024-00889-z
Markus Schlarb
{"title":"Rolling reductive homogeneous spaces","authors":"Markus Schlarb","doi":"10.1007/s13324-024-00889-z","DOIUrl":"10.1007/s13324-024-00889-z","url":null,"abstract":"<div><p>Rollings of reductive homogeneous spaces are investigated. More precisely, for a reductive homogeneous space <i>G</i>/<i>H</i> with reductive decomposition <span>(mathfrak {{g}} = mathfrak {{h}} oplus mathfrak {{m}})</span>, we consider rollings of <span>(mathfrak {{m}})</span> over <i>G</i>/<i>H</i> without slip and without twist, where <i>G</i>/<i>H</i> is equipped with an invariant covariant derivative. To this end, an intrinsic point of view is taken, meaning that a rolling is a curve in the configuration space <i>Q</i> which is tangent to a certain distribution. By considering an <i>H</i>-principal fiber bundle <span>(overline{pi }:overline{Q}rightarrow Q)</span> over the configuration space equipped with a suitable principal connection, rollings of <span>(mathfrak {{m}})</span> over <i>G</i>/<i>H</i> can be expressed in terms of horizontally lifted curves on <span>(overline{Q})</span>. The total space of <span>(overline{pi }:overline{Q}rightarrow Q)</span> is a product of Lie groups. In particular, for a given control curve, this point of view allows for characterizing rollings of <span>(mathfrak {{m}})</span> over <i>G</i>/<i>H</i> as solutions of an explicit, time-variant ordinary differential equation (ODE) on <span>(overline{Q})</span>, the so-called kinematic equation. An explicit solution for the associated initial value problem is obtained for rollings with respect to the canonical invariant covariant derivative of first and second kind if the development curve in <i>G</i>/<i>H</i> is the projection of a one-parameter subgroup in <i>G</i>. Lie groups and Stiefel manifolds are discussed as examples.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00889-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Limiting behaviors of constrained minimizers for the mass subcritical fractional NLS equations 质量次临界分数 NLS方程受约束最小化的极限行为
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-03-25 DOI: 10.1007/s13324-024-00899-x
Jie Yang, Haibo Chen, Lintao Liu
{"title":"Limiting behaviors of constrained minimizers for the mass subcritical fractional NLS equations","authors":"Jie Yang,&nbsp;Haibo Chen,&nbsp;Lintao Liu","doi":"10.1007/s13324-024-00899-x","DOIUrl":"10.1007/s13324-024-00899-x","url":null,"abstract":"<div><p>In this paper, we study the asymptotic properties of solutions for the constrained minimization problems. </p><div><div><span>$$begin{aligned} d_{b_p}(p):=inf _{{uin H^s_V({mathbb {R}}^2): int _{{mathbb {R}}^2}|u|^2dx=1}}I_{p,b_p}(u), end{aligned}$$</span></div></div><p>where <span>(sin (frac{1}{2},1),)</span> <span>(pin (0, 2s))</span>, <span>(b_p&gt;0)</span> and </p><div><div><span>$$begin{aligned} I_{p,b_p}(u){:=}frac{1}{2}int _{{mathbb {R}}^2}left( |(-Delta )^{frac{s}{2}}u|^2{+}V(x)|u|^2right) dx{-}frac{b_p}{p+2}int _{{mathbb {R}}^2}|u|^{p+2}dx,quad uin H^s_V({mathbb {R}}^2). end{aligned}$$</span></div></div><p>First, when <span>(lim _{pnearrow 2s}b_p=b&lt;b^*)</span>, the set of minimizers of <span>(d_{b_p}(p))</span> is compact in a suitable space as <span>(pnearrow 2s)</span>. In addition, when <span>(lim _{pnearrow 2s}b_p=bge b^*)</span>, by developing suitable trial functions for some fine energy estimates, we prove that all minimizers must blow up and give decay properties of minimizers.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A mathematical description of the Weber nucleus as a classical and quantum mechanical system 韦伯原子核作为经典和量子力学系统的数学描述
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-03-25 DOI: 10.1007/s13324-024-00891-5
Urs Frauenfelder, Joa Weber
{"title":"A mathematical description of the Weber nucleus as a classical and quantum mechanical system","authors":"Urs Frauenfelder,&nbsp;Joa Weber","doi":"10.1007/s13324-024-00891-5","DOIUrl":"10.1007/s13324-024-00891-5","url":null,"abstract":"<div><p>Wilhelm Weber’s electrodynamics is an action-at-a-distance theory which has the property that equal charges inside a critical radius become attractive. Weber’s electrodynamics inside the critical radius can be interpreted as a classical Hamiltonian system whose kinetic energy is, however, expressed with respect to a <i>Lorentzian</i> metric. In this article we study the Schrödinger equation associated with this Hamiltonian system, and relate it to Weyl’s theory of singular Sturm–Liouville problems.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00891-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140210243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Eigenvalue problem versus Casimir functions for Lie algebras Lie 架构的特征值问题与卡西米尔函数
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-03-25 DOI: 10.1007/s13324-024-00892-4
Alina Dobrogowska, Marzena Szajewska
{"title":"Eigenvalue problem versus Casimir functions for Lie algebras","authors":"Alina Dobrogowska,&nbsp;Marzena Szajewska","doi":"10.1007/s13324-024-00892-4","DOIUrl":"10.1007/s13324-024-00892-4","url":null,"abstract":"<div><p>We present a new perspective on the invariants of Lie algebras (Casimir functions). Our approach is based on the connection of a linear mapping <span>(Fin End(V))</span>, which has a given eigenvector <i>v</i>, to a Lie algebra. We obtain a solvable Lie algebra by considering a single pair (<i>F</i>, <i>v</i>). However, by considering a set of such pairs <span>((F_i, v_i))</span>, <span>(i=1,2,ldots , s)</span>, we can obtain any finite-dimensional Lie algebra. We also describe the Casimir function equations in terms of pairs, since the eigenvalue problem of (<i>F</i>, <i>v</i>) yields a Lie bracket. We outline the criterion for the quantity of Casimirs and their formulas for any Lie algebra, which depends on the decomposability of the tensor built from the pairs <span>((F_i,v_i))</span>. In addition, we present the meaning of lifting Lie algebras in this context and explain how to construct Casimir functions for the lifted Lie algebra based on Casimir functions for the initial Lie algebra. One of the main results of the paper is to present the method to identify all Casimirs for a lifted Lie algebra starting from the initial one.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Toda and Laguerre–Freud equations and tau functions for hypergeometric discrete multiple orthogonal polynomials 超几何离散多重正交多项式的 Toda 和 Laguerre-Freud 方程及 tau 函数
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-03-24 DOI: 10.1007/s13324-024-00876-4
Itsaso Fernández-Irisarri, Manuel Mañas
{"title":"Toda and Laguerre–Freud equations and tau functions for hypergeometric discrete multiple orthogonal polynomials","authors":"Itsaso Fernández-Irisarri,&nbsp;Manuel Mañas","doi":"10.1007/s13324-024-00876-4","DOIUrl":"10.1007/s13324-024-00876-4","url":null,"abstract":"<div><p>In this paper, the authors investigate the case of discrete multiple orthogonal polynomials with two weights on the step line, which satisfy Pearson equations. The discrete multiple orthogonal polynomials in question are expressed in terms of <span>(tau )</span>-functions, which are <i>double</i> Wronskians of generalized hypergeometric series. The shifts in the spectral parameter for type II and type I multiple orthogonal polynomials are described using banded matrices. It is demonstrated that these polynomials offer solutions to multicomponent integrable extensions of the nonlinear Toda equations. Additionally, the paper characterizes extensions of the Nijhoff–Capel totally discrete Toda equations. The hypergeometric <span>(tau )</span>-functions are shown to provide solutions to these integrable nonlinear equations. Furthermore, the authors explore Laguerre–Freud equations, nonlinear equations for the recursion coefficients, with a particular focus on the multiple Charlier, generalized multiple Charlier, multiple Meixner II, and generalized multiple Meixner II cases.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00876-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Beam deflection coupled systems of fractional differential equations: existence of solutions, Ulam–Hyers stability and travelling waves 分微分方程的梁偏转耦合系统：解的存在性、Ulam-Hyers 稳定性和行波
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-03-19 DOI: 10.1007/s13324-024-00890-6
Kamel Bensassa, Zoubir Dahmani, Mahdi Rakah, Mehmet Zeki Sarikaya
{"title":"Beam deflection coupled systems of fractional differential equations: existence of solutions, Ulam–Hyers stability and travelling waves","authors":"Kamel Bensassa,&nbsp;Zoubir Dahmani,&nbsp;Mahdi Rakah,&nbsp;Mehmet Zeki Sarikaya","doi":"10.1007/s13324-024-00890-6","DOIUrl":"10.1007/s13324-024-00890-6","url":null,"abstract":"<div><p>In this paper, we study a coupled system of beam deflection type that involves nonlinear equations with sequential Caputo fractional derivatives. Under flexible/fixed end-conditions, two main theorems on the existence and uniqueness of solutions are proved by using two fixed point theorems. Some examples are discussed to illustrate the applications of the existence and uniqueness of solution results. Another main result on the Ulam–Hyers stability of solutions for the introduced system is also discussed. Some examples of stability are discussed. New travelling wave solutions are obtained for another conformable coupled system of beam type that has a connection with the first considered system. A conclusion follows at the end.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00890-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140167943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","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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