Russian Journal of Mathematical Physics最新文献_第2页

Uniform Spectral Asymptotics for the Schrödinger Operator with Translation in Free Term and Periodic Boundary Conditions 自由项和周期边界条件下具有平移的Schrödinger算子的一致谱渐近性

IF 1.5 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI: 10.1134/S1061920825600552

D.I. Borisov, D.M. Polyakov

{"title":"Uniform Spectral Asymptotics for the Schrödinger Operator with Translation in Free Term and Periodic Boundary Conditions","authors":"D.I. Borisov, D.M. Polyakov","doi":"10.1134/S1061920825600552","DOIUrl":"10.1134/S1061920825600552","url":null,"abstract":" We consider a nonlocal Schrödinger operator on the interval ((0,2pi)) with the periodic boundary conditions and a translation in the free term. The value of the translation is denoted by (a) and is treated as a parameter. We show that the resolvent of such an operator is Hölder continuous in this parameter with the exponent (frac{1}{2},) the spectrum of this operator consists of infinitely many discrete eigenvalues accumulating at infinity, and all eigenvalues are continuous in (ain[0,2pi]) and coincide for (a=0) and (a=2pi.) Our main result is a uniform spectral asymptotics for the operator under consideration. Namely, we show that sufficiently large eigenvalues separate into pairs, each is located in the vicinity of the point (n^2,) where (n) in the index counting the eigenvalues, and we find a four-term asymptotics for these eigenvalues for large (n) with the error term of order (O(n^{-3})), and this term is uniform with respect to (a.) We also discuss nontrivial high-frequency phenomena demonstrated by the uniform spectral asymptotics we have found. DOI 10.1134/S1061920825600552 ","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 3","pages":"434 - 450"},"PeriodicalIF":1.5,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145184075","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

Continuously Irreducibly Representable Groups with Irreducible Representations of Bounded Degree 具有有界度不可约表示的连续不可约可表示群

IF 1.5 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI: 10.1134/S106192082503015X

A.I. Shtern

引用次数: 0

On the Reconstruction from the Imaginary Part for Radiation Solutions in Two Dimensions 二维辐射解的虚部重构

IF 1.5 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI: 10.1134/S1061920825601077

A.V. Nair, R.G. Novikov

引用次数: 0

Defuzzification and Joint Measurability of Quantum Fuzzy Observables 量子模糊观测的解模糊化与联合可测性

IF 1.5 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI: 10.1134/S1061920825600692

R. Beneduci

{"title":"Defuzzification and Joint Measurability of Quantum Fuzzy Observables","authors":"R. Beneduci","doi":"10.1134/S1061920825600692","DOIUrl":"10.1134/S1061920825600692","url":null,"abstract":" Commutative positive operator-valued measures (POVMs) are fuzzifications of spectral measures. In quantum mechanics, this corresponds to a connection between commutative unsharp observables (represented by commutative POVMs) and sharp observables (represented by self-adjoint operators); the former being a fuzzification of the latter. We prove that commutative unsharp observables can be defuzzified in order to obtain the sharp observables of which they are the fuzzy versions. We prove this in the case of POVMs defined on a general topological space which we require to be second countable and metrizable, generalizing some previous results on real POVMs. Then, we analyze some of the consequences of this defuzzification procedure. In particular we show that the joint measurability of two commutative (but generally not commuting) POVMs (F_1) and (F_2) corresponds to the existence of two commuting self-adjoint operators (A^+_1) and (A^+_2) in an extended Hilbert space (mathcal{H}^+) whose projections are the sharp versions of (F_1) and (F_2), respectively. In other words, the joint measurability of (F_1) and (F_2) is translated in the commutativity of (A_1^+) and (A_2^+). This is proved for POVMs on a second countable, Hausdorff, locally compact topological space, generalizing similar results obtained in the case of real POVMs. DOI 10.1134/S1061920825600692 ","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 3","pages":"426 - 433"},"PeriodicalIF":1.5,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145184069","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 Mathematical Theory of Quantum Stochastic Filtering Equations for Mixed States 混合态量子随机滤波方程的数学理论

IF 1.5 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI: 10.1134/S1061920825600825

V.N. Kolokoltsov

引用次数: 0

Random Homogenization of Lavrentiev–Bitsadze Equation in Partially Perforated Domain 部分穿孔区域Lavrentiev-Bitsadze方程的随机均匀化

IF 1.5 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI: 10.1134/S1061920825600813

E.A. Akimova, G.A. Chechkin

引用次数: 0

Double-Deck Structure of the Boundary Layer in the Flow Around a Small Localized Irregularity on a Curved Surface 曲面上局部小不规则流动中边界层的双层结构

IF 1.5 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI: 10.1134/S1061920825600461

R.K. Gaydukov

引用次数: 0

On One Class of Vector Continued Fractions with Operator Elements and the Jacobi–Perron Algorithm 一类带算子元的矢量连分数及其Jacobi-Perron算法

IF 1.5 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI: 10.1134/S1061920825030148

A.S. Osipov

{"title":"On One Class of Vector Continued Fractions with Operator Elements and the Jacobi–Perron Algorithm","authors":"A.S. Osipov","doi":"10.1134/S1061920825030148","DOIUrl":"10.1134/S1061920825030148","url":null,"abstract":" We consider a class of infinite vector continued fractions of a complex variable such that their coefficients are bounded operators in a Hilbert space. They may be regarded as analogs (in a broad sense) of (J)-fractions used in the theory of Jacobi operators and the classical moment problem. To each of the continued fractions under consideration, there corresponds the band operator generated by certain infinite block matrix containing a finite number of nonzero diagonals, which are composed of the (operator) elements of this continued fraction. Using the inverse spectral theory for these band operators, we establish the main properties of such continued fractions, in particular, their expansion algorithm and the criterion for existence of this expansion. It turns out that the algorithm of reconstruction of a band operator from its spectral data (the moment sequence of its Weyl function) can be regarded as a modified version of a known Jacobi-Perron expansion algorithm, applied to a system of operator-functions holomorphic at infinity in order to get a continued fraction from the class under study. Certain issues of the theory of Hermite-Padé approximants, related to the studied subject, are also considered. DOI 10.1134/S1061920825030148 ","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 3","pages":"562 - 582"},"PeriodicalIF":1.5,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145184079","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

The Topology of Uniform Convergence on a Group Is Discrete for Unitary Representations of Amenable Groups 对于可服从群的幺正表示，群上一致收敛的拓扑是离散的

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/S1061920825020153

A.I. Shtern

引用次数: 0

Short-Wave Asymptotic Solutions of the Wave Equation with Localized Velocity Perturbations Whose Wavelength is not Comparable to the Scale of the Localized Inhomogeneity. 波长与局域非均匀性尺度不可比的局域速度扰动波动方程的短波渐近解。

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/S1061920825600916

A.I. Allilueva, A.I. Shafarevich

引用次数: 0