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Russian Journal of Mathematical Physics最新文献

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Nonself-adjoint Three-Dimensional Operators with Point Interactions Supported by Curves 曲线支持点相互作用的非自伴三维算子
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S1061920826020044
D.I. Borisov
{"title":"Nonself-adjoint Three-Dimensional Operators with Point Interactions Supported by Curves","authors":"D.I. Borisov","doi":"10.1134/S1061920826020044","DOIUrl":"10.1134/S1061920826020044","url":null,"abstract":"<p> In a general three-dimensional domain we consider a second order differential operator with variable coefficients subject to an arbitrary boundary condition; the operator is supposed to be <span>(m)</span>-sectorial. We show how to add a point interaction supported by a given curve <span>( Gamma )</span> with a complex-valued coupling function to this operator. We provide a rigorous way for defining such an operator with point interaction and study its basic properties. Our approach is based on the main idea used to define the Laplacian in the three-dimensional space on a given curve, but we modify this idea quite essentially avoiding at the same time any implicit Green functions. Our definition provides an effective tool for studying general operators in three-dimensional domains with point interactions on given curves. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"241 - 262"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458757","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
Scattering for Anisotropic Potentials 各向异性势的散射
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S1061920826600443
E. Korotyaev
{"title":"Scattering for Anisotropic Potentials","authors":"E. Korotyaev","doi":"10.1134/S1061920826600443","DOIUrl":"10.1134/S1061920826600443","url":null,"abstract":"<p> We consider the scattering for the operator <span>(H=H_0+V)</span>, where the unperturbed operator <span>(H_0)</span> is not assumed to be elliptic and the potential <span>(V)</span> is anisotropic. Under some conditions on <span>(H_0)</span> and <span>(V)</span>, we show that the wave operators for <span>(H_0)</span> and <span>(H)</span> exist and are complete, <span>(H)</span> has no singular continuous spectrum, and the eigenvalues of <span>(H)</span> can accumulate only to zero. Under stronger conditions on <span>(V)</span>, the operator <span>(H)</span> has finitely many eigenvalues only. These results are applied to the invariance principle and for time-dependent potentials. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"340 - 356"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458978","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
Inverse Semigroup of Metrics on a Double is Fundamental 双上度量的逆半群是基本的
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-03-27 DOI: 10.1134/S1061920825601958
V. Manuilov
{"title":"Inverse Semigroup of Metrics on a Double is Fundamental","authors":"V. Manuilov","doi":"10.1134/S1061920825601958","DOIUrl":"10.1134/S1061920825601958","url":null,"abstract":"<p> We show that the inverse semigroup of equivalence classes of metrics on two copies of a metric space is fundamental. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"126 - 128"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561966","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
New Numerical Invariants of an Unfolding of a Polycycle “Tears of the Heart” 多环“心之泪”展开的新数值不变量
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-03-27 DOI: 10.1134/S1061920826600170
Yu.S. Ilyashenko, S. Minkov, I. Shilin
{"title":"New Numerical Invariants of an Unfolding of a Polycycle “Tears of the Heart”","authors":"Yu.S. Ilyashenko,&nbsp;S. Minkov,&nbsp;I. Shilin","doi":"10.1134/S1061920826600170","DOIUrl":"10.1134/S1061920826600170","url":null,"abstract":"<p> In this paper, new numerical invariants of structurally unstable vector fields in the plane are found. One of the main tools is an improved asymptotics of sparkling saddle connections that occur when a separatrix loop of a hyperbolic saddle breaks. Another main tool is a new topological invariant of two arithmetic progressions, both perturbed and unperturbed, on the real line. For the pairs of the unperturbed arithmetic progressions, we give a complete topological classification. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"89 - 106"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561964","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 Dissipation Operators of Quantum Optics 量子光学的耗散算子
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-03-27 DOI: 10.1134/S1061920826600121
A.I. Komech, E.A. Kopylova
{"title":"On Dissipation Operators of Quantum Optics","authors":"A.I. Komech,&nbsp;E.A. Kopylova","doi":"10.1134/S1061920826600121","DOIUrl":"10.1134/S1061920826600121","url":null,"abstract":"<p> We consider dissipation operators used in Quantum Optics for the description of quantum spontaneous emission in the context of damped driven Jaynes–Cummings equations. The equations describe quantized one-mode Maxwell field coupled to a two-level molecule. </p><p> The nonpositivity of two basic dissipation operators is proved in the framework of the theory of the Hilbert space of the Hilbert–Schmidt operators. We show that one of the operators is symmetric, while the other is not. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"107 - 109"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147558981","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
Asymptotics of the Transfer Function of the Poincar(acute{text{e}})–Steklov Operator for a Functionally Graded Elastic Layer 泛函梯度弹性层的Poincar - (acute{text{e}}) -Steklov算子传递函数的渐近性
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-03-27 DOI: 10.1134/S1061920825601193
A.A. Bobylev
{"title":"Asymptotics of the Transfer Function of the Poincar(acute{text{e}})–Steklov Operator for a Functionally Graded Elastic Layer","authors":"A.A. Bobylev","doi":"10.1134/S1061920825601193","DOIUrl":"10.1134/S1061920825601193","url":null,"abstract":"<p> We consider the Poincaré–Steklov operator for a three-dimensional boundary-value problem for a functionally graded elastic layer, which maps normal stresses into normal displacements on a part of the boundary. A three-term asymptotic expansion of the transfer function of this operator is obtained for large values of the Fourier transform parameters. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"34 - 41"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561547","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 an Extremal Gheit Function and Its Applications 极值Gheit函数及其应用
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-03-27 DOI: 10.1134/S106192082560165X
N.A. Ilyasov, A.R. Alimov
{"title":"On an Extremal Gheit Function and Its Applications","authors":"N.A. Ilyasov,&nbsp;A.R. Alimov","doi":"10.1134/S106192082560165X","DOIUrl":"10.1134/S106192082560165X","url":null,"abstract":"<p> We find exact orders of decrease of quantities that characterize various properties of <span>(2pi)</span>-periodic summable functions on a class with given majorant of the second-order modulus of continuity. We show that all these quantities have the same order of decrease (with a single condition on the behavior of the majorant), which is attained on a singe extremal function. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"1 - 11"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561783","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
Three Identical One-Dimensional Quantum Particles with Point Interaction as a Solvable Model: II. Negative Essential Spectrum 具有点相互作用的三个相同的一维量子粒子的可解模型：ⅱ。负本质谱
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-03-27 DOI: 10.1134/S1061920825601740
M.A. Lyalinov
{"title":"Three Identical One-Dimensional Quantum Particles with Point Interaction as a Solvable Model: II. Negative Essential Spectrum","authors":"M.A. Lyalinov","doi":"10.1134/S1061920825601740","DOIUrl":"10.1134/S1061920825601740","url":null,"abstract":"<p> This is the second part of our work dealing with spectral analysis for the Hamiltonian of three identical one-dimensional quantum particles. The Hamiltonian is represented as a sum of Laplacian and a singular delta-potential with the symmetric support consisting of six half-lines (leads) with the same origin. Contrary to the first part discussing the discrete spectrum and the eigenfunctions, the second part is devoted to study of the negative essential spectrum and the corresponding generalized eigenfunctions. It turns out that, instead of the Kontorovich–Lebedev integral representation exploited for the eigenfunctions of the discrete spectrum, alternative integral representations of the Watson–Bessel type for the generalized eigenfunctions of the essential spectrum are applied. As in the first part, the symmetry of the support of the corresponding singular potential is made use of. The operator is decomposed to the fibers by means of the Fourier transform on the group of symmetry. Further analysis is connected with the investigation of the problem for the fibers and leads to the study of spectral properties of a functional equation similar to that for the Maryland model. The results obtained here enable one to determine explicit formulas for the generalized eigenfunction and to study their behavior at far distances by means of reduction to the Sommerfeld integral representations. The far field asymptotics of the generalized eigenfunctions are interpreted as surface waves localized near the leads of the support of the singular potential. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"110 - 125"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561784","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
Singularities of Landau–Ginzburg Models for Complete Intersections and Derived Categories 完全交点和派生范畴的Landau-Ginzburg模型的奇异性
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-03-27 DOI: 10.1134/S1061920825601405
V.V. Przyjalkowski
{"title":"Singularities of Landau–Ginzburg Models for Complete Intersections and Derived Categories","authors":"V.V. Przyjalkowski","doi":"10.1134/S1061920825601405","DOIUrl":"10.1134/S1061920825601405","url":null,"abstract":"<p> The mirror symmetry predicts that the bounded derived category of a smooth Fano variety is equivalent to the Fukaya–Seidel category of its Landau–Ginzburg model. It is expected that the fibers of Landau–Ginzburg model with ordinary double points correspond to an exceptional collection of a Fano variety. We verify this expectation at a numerical level for Fano complete intersections and Calabi–Yau compactifications of their toric Landau–Ginzburg models of Givental’s type. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"155 - 162"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561785","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
Quantization of Branched Coverings Revisited 再论分支覆盖的量化
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-03-27 DOI: 10.1134/S1061920825601752
E. Troitsky
{"title":"Quantization of Branched Coverings Revisited","authors":"E. Troitsky","doi":"10.1134/S1061920825601752","DOIUrl":"10.1134/S1061920825601752","url":null,"abstract":"<p> We address the problem of identification of branched coverings (continuous open surjections <span>(pcolon Yto X)</span> of Hausdorff spaces with uniformly bounded number of pre-images) with faithful unital positive conditional expectations <span>(Ecolon C(Y)to C(X))</span> topologically of index-finite type. Caused by recent progress (A. Chirvasitu, 2024) in the field and detection of an issue in our old paper, we revisit it to make some advances. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"189 - 193"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561967","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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