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The General Kastler–Kalau–Walze Type Theorem for the (J)-Twist (D_{J}) of the Dirac Operator 狄拉克算子(J) -Twist (D_{J})的一般Kastler-Kalau-Walze型定理
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-07-29 DOI: 10.1134/S1061920824601204
Siyao Liu, Yong Wang
{"title":"The General Kastler–Kalau–Walze Type Theorem for the (J)-Twist (D_{J}) of the Dirac Operator","authors":"Siyao Liu,&nbsp;Yong Wang","doi":"10.1134/S1061920824601204","DOIUrl":"10.1134/S1061920824601204","url":null,"abstract":"<p> In [21] and [22], we proved the Kastler–Kalau–Walze type theorem for the <span>(J)</span>-twist <span>(D_{J})</span> of the Dirac operator on <span>(3)</span>-dimensional, <span>(4)</span>-dimensional, and <span>(6)</span>-dimensional almost product Riemannian spin manifolds with boundary. In this paper, we generalize our previous conclusions and establish the proof of the general Kastler–Kalau–Walze type theorem for the <span>(J)</span>-twist <span>(D_{J})</span> of the Dirac operator on any even-dimensional almost product Riemannian spin manifold with boundary. </p><p> <b> DOI</b> 10.1134/S1061920824601204 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 2","pages":"341 - 364"},"PeriodicalIF":1.5,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Interaction of Relativistic Particles with Singular Potentials Supported by a Periodic Graph 周期图支持奇异势的相对论粒子的相互作用
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-07-29 DOI: 10.1134/S1061920825600163
V.S. Rabinovich
{"title":"Interaction of Relativistic Particles with Singular Potentials Supported by a Periodic Graph","authors":"V.S. Rabinovich","doi":"10.1134/S1061920825600163","DOIUrl":"10.1134/S1061920825600163","url":null,"abstract":"<p> We consider the interaction of relativistic particles described by two-dimensional Dirac operators with delta-type singular potentials supported by periodic graphs <span>(Gammasubsetmathbb{R}^{2})</span>. This problem can be regarded as a relativistic analog of the Kronig–Penney model of electron propagation in solid state physics. We associate with this problem an unbounded operator in the Hilbert space <span>(L^{2}(mathbb{R}^{2},mathbb{C}^{2}))</span>. The study of spectral properties of these operators is reduced to the study of the Fredholmness of singular integral operators on the graph <span>(Gamma)</span>. We obtain necessary and sufficient conditions for the Fredholmness of these operators as ellipticity conditions on the edges, matrix conditions at the vertices, and conditions of invertibility of limit operators which are periodic operators on the graph <span>(Gamma)</span>. We apply the Bloch–Floquet theory to the study of invertibility of limit operators. </p><p> <b> DOI</b> 10.1134/S1061920825600163 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 2","pages":"365 - 378"},"PeriodicalIF":1.5,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Orbits of the Action of the Gauge Group 轨距群作用的轨道
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-07-29 DOI: 10.1134/S1061920825020037
V.K. Beloshapka
{"title":"Orbits of the Action of the Gauge Group","authors":"V.K. Beloshapka","doi":"10.1134/S1061920825020037","DOIUrl":"10.1134/S1061920825020037","url":null,"abstract":"<p> Differential-algebraic descriptions of the orbits of the action of the gauge group for some differential-algebraic sets and functions are constructed. In all cases considered here, it is shown that the orbit is a differential-algebraic set. Applications of the constructed criteria are given. </p><p> <b> DOI</b> 10.1134/S1061920825020037 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 2","pages":"239 - 244"},"PeriodicalIF":1.5,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Semiclassical Trace Formula for the Bochner–Schrödinger Operator Bochner-Schrödinger算子的半经典轨迹公式
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-07-29 DOI: 10.1134/S1061920825600333
Yu.A. Kordyukov
{"title":"Semiclassical Trace Formula for the Bochner–Schrödinger Operator","authors":"Yu.A. Kordyukov","doi":"10.1134/S1061920825600333","DOIUrl":"10.1134/S1061920825600333","url":null,"abstract":"<p> We study the semiclassical Bochner–Schrödinger operator <span>(H_{p}=frac{1}{p^2}Delta^{L^potimes E}+V)</span> on tensor powers <span>(L^p)</span> of a Hermitian line bundle <span>(L)</span> twisted by a Hermitian vector bundle <span>(E)</span> on a Riemannian manifold of bounded geometry. For any function <span>(varphiin C^infty_c(mathbb R))</span>, we consider the bounded linear operator <span>(varphi(H_p))</span> in <span>(L^2(X,L^potimes E))</span> defined by the spectral theorem. We prove that its smooth Schwartz kernel on the diagonal admits a complete asymptotic expansion in powers of <span>(p^{-1})</span> in the semiclassical limit <span>(pto infty)</span>. In particular, when the manifold is compact, we get a complete asymptotic expansion for the trace of <span>(varphi(H_p))</span>. </p><p> <b> DOI</b> 10.1134/S1061920825600333 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 2","pages":"297 - 313"},"PeriodicalIF":1.5,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantum Time Travel Revisited: Noncommutative Möbius Transformations and Time Loops 量子时间旅行重访：非交换Möbius转换和时间循环
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-07-29 DOI: 10.1134/S1061920824601691
J.E. Gough
{"title":"Quantum Time Travel Revisited: Noncommutative Möbius Transformations and Time Loops","authors":"J.E. Gough","doi":"10.1134/S1061920824601691","DOIUrl":"10.1134/S1061920824601691","url":null,"abstract":"<p> We extend the theory of quantum time loops introduced by Greenberger and Svozil [1] from the scalar situation (where paths have just an associated complex amplitude) to the general situation where the time traveling system has multidimensional underlying Hilbert space. The main mathematical tool that emerges is the noncommutative Möbius Transformation and this affords a formalism similar to the modular structure well known to feedback control problems. The self-consistency issues that plague other approaches do not arise here, as we do not consider completely closed time loops. We argue that a sum-over-all-paths approach may be carried out in the scalar case but quickly becomes unwieldy in the general case. It is natural to replace the beam splitters of [1] with more general components having their own quantum structure, in which case the theory starts to resemble the quantum feedback network theory for open quantum optical models and indeed we exploit this to look at more realistic physical models of time loops. We analyze some Grandfather paradoxes in the new setting. </p><p> <b> DOI</b> 10.1134/S1061920824601691 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 2","pages":"251 - 264"},"PeriodicalIF":1.5,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximative Compactness and Acting Points 近似紧致性与作用点
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-07-29 DOI: 10.1134/S1061920825600527
A.R. Alimov, N.A. Ilyasov
{"title":"Approximative Compactness and Acting Points","authors":"A.R. Alimov,&nbsp;N.A. Ilyasov","doi":"10.1134/S1061920825600527","DOIUrl":"10.1134/S1061920825600527","url":null,"abstract":"<p> It is shown that, in many problems of geometric approximation theory related to min- and max-approximative compactness, it suffices to consider not the entire unit sphere, but rather its only part consisting of acting points (for a given set <span>(M)</span>) — these being the points of the unit sphere such that <span>(M)</span> can be touched by an “analog” of such a point on some homothetic copy of the unit ball. CLUR- and VDS-point for a set are introduced, and their relations to points of min- and max- approximative (norm, weak) compactness are studied. In terms of these points, balayage theorems for problems of min- and max- approximative (norm, weak) compactness of suns and max-suns are obtained. </p><p> <b> DOI</b> 10.1134/S1061920825600527 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 2","pages":"219 - 227"},"PeriodicalIF":1.5,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solarity of Boundedly ae-Compact Sets 有界ae-紧集的太阳性
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-07-29 DOI: 10.1134/S1061920825020165
I.G. Tsar’kov
{"title":"Solarity of Boundedly ae-Compact Sets","authors":"I.G. Tsar’kov","doi":"10.1134/S1061920825020165","DOIUrl":"10.1134/S1061920825020165","url":null,"abstract":"<p> We study boundedly ae-compact sets admitting, for any <span>(varepsilon&gt;0)</span>, an <span>(ntau)</span>-continuous <span>(varepsilon)</span>-selection, where <span>(tau)</span> is the topology of convergence in measure. Any such set in <span>(L_p)</span>, <span>(1leqslant p&lt;infty)</span>, is shown to be a sun. Given a nonempty set, it is shown that the existence of an <span>(ntau)</span>-continuous <span>(varepsilon)</span>-selection for each <span>(varepsilon&gt;0)</span> is equivalent to existence of a norm-norm continuous <span>(varepsilon)</span>-selection for each <span>(varepsilon&gt;0)</span>. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 2","pages":"410 - 415"},"PeriodicalIF":1.5,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Resonances and Scattering by a Periodic Structure 周期结构的共振和散射
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-07-29 DOI: 10.1134/S1061920825600497
D.I. Borisov, A.A. Fedotov
{"title":"Resonances and Scattering by a Periodic Structure","authors":"D.I. Borisov,&nbsp;A.A. Fedotov","doi":"10.1134/S1061920825600497","DOIUrl":"10.1134/S1061920825600497","url":null,"abstract":"<p> We consider a Schrödinger operator on the real line with a super-exponentially decaying and oscillating potential <span>(V(x)=e^{-x^2}big(a-b e^{2 mathrm{i} alpha x}big))</span>, where <span>(a,bin mathbb Csetminus{0})</span> and <span>(alpha&gt;0)</span> are parameters. Let <span>(k^2)</span> be a spectral parameter. On the complex plane of <span>(k)</span>, we find four infinite vertical sequences of resonances of this operator and four finite sequences of resonances located along certain rays in the complex plane. We obtain asymptotic representations for the resonances located far from the origin. The leading terms in the representations are found explicitly, while the error terms are estimated uniformly in <span>(a)</span> and <span>(b)</span>. For certain values of the parameters, on the complex plane of <span>(k^2)</span>, the vertical sequences might turn into sequences located near the real line, and thus, probably might be interesting for applications in physics. </p><p> <b> DOI</b> 10.1134/S1061920825600497 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 2","pages":"245 - 250"},"PeriodicalIF":1.5,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Riccati Difference Equation and Continued Fractions 论Riccati差分方程与连分式
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-07-29 DOI: 10.1134/S1061920824601538
A.V. Ivanov
{"title":"On the Riccati Difference Equation and Continued Fractions","authors":"A.V. Ivanov","doi":"10.1134/S1061920824601538","DOIUrl":"10.1134/S1061920824601538","url":null,"abstract":"<p> We consider a Riccati difference equation <span>(Phi(x) + rho(x)/Phi(x-omega) = v(x))</span> under the assumption that coefficients <span>(rho)</span>, <span>(v)</span> are <span>(1)</span>-periodic continuous functions of a real variable and <span>(omega)</span> is an irrational parameter. By using a connection between continued fraction theory and theory of <span>(SL(2,mathbb{R}))</span>-cocycles over irrational rotation, we investigate the problem of existence of continuous solutions to this equation. It is shown that the convergence of a continued fraction representing a solution to the Riccati equation can be expressed in terms of hyperbolicity of the cocycle naturally associated to this continued fraction. We establish sufficient conditions for the uniform hyperbolicity of a <span>(SL(2,mathbb{R}))</span>-cocycle, which imply the convergence of the corresponding continued fraction. The results thus obtained, along with the critical set method, have been applied to a special class of Riccati equations <span>(rho(x)equiv 1, v(x) = g b(x), ggg 1,)</span> to obtain sufficient conditions for the existence of continuous solutions in this case. </p><p> <b> DOI</b> 10.1134/S1061920824601538 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 2","pages":"265 - 287"},"PeriodicalIF":1.5,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hyperbolic Property of a Linear Volterra Integro-Differential Operator in Problems of Oscillations of a Viscoelastic Rod 粘弹性杆振动问题中线性Volterra积分-微分算子的双曲性质
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-07-29 DOI: 10.1134/S106192082502013X
N.A. Rautian, D.V. Georgievskii
{"title":"Hyperbolic Property of a Linear Volterra Integro-Differential Operator in Problems of Oscillations of a Viscoelastic Rod","authors":"N.A. Rautian,&nbsp;D.V. Georgievskii","doi":"10.1134/S106192082502013X","DOIUrl":"10.1134/S106192082502013X","url":null,"abstract":"<p> For Volterra integro-differential operators in partial derivatives of the second order, the concept of hyperbolicity with respect to a cone is introduced. It is established that the hyperbolicity with respect to a cone is equivalent to the localization of the support of the fundamental solution of the Volterra integro-differential operator in the conjugate cone. The hyperbolicity with respect to a cone of the integro-differential operator of oscillations of a viscoelastic rod with a fractional-exponential relaxation function is proved. </p><p> <b> DOI</b> 10.1134/S106192082502013X </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 2","pages":"386 - 398"},"PeriodicalIF":1.5,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","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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