SwePub - search: WFRF:(Kurasov Pavel)

Enumeration	Reference	Cover	Find
1.	Kurasov, Pavel, et al. (author) Second Virial Coefficient for One-dimensional System 1994 In: NATO ASI Series, Series B: Physics. - 0258-1221. - 0306447045 ; 324, s. 423-428 Conference paper (peer-reviewed)
2.	Kurasov, Pavel, et al. (author) Surfaces with an Internal Structure 1989 In: Lecture Notes in Physics : Applications of Self-Adjoint Extensions in Quantum Physics: Proceedings of a Conference Held at the Laboratory of Theoretical Physics. ; 324, s. 177-193 Conference paper (peer-reviewed)
3.	Kurasov, Pavel, et al. (author) Three One-dimensional Bosons with an Internal Structure 1988 In: Schrödinger operators, standard and nonstandard. - 9971508400 ; , s. 166-188 Conference paper (peer-reviewed)abstract A model of scattering of three one-dimensional particles is constructed by means of the extension theory of selfadjoint operators. The dispersion equation for the three-particle bound state energy is obtained and an exact mathematical expression for the corresponding wave functions is derived
4.	Albeverino, S., et al. (author) Pseudo-Differential Operators with Point Interactions 1997 In: Letters in Mathematical Physics. - 0377-9017 .- 1573-0530. ; 41, s. 79-92 Journal article (peer-reviewed)abstract Point interactions for pseudo-differential operators are studied. Necessary and sufficient conditions for a pseudo-differential operator to have nontrivial point perturbations are given. The results are applied to the construction of relativistic spin zero Hamiltonians with point interactions.
5.	Albeverio, S., et al. (author) Finite rank perturbations and distribution theory 1999 In: Proceedings of the American Mathematical Society. - 0002-9939 .- 1088-6826. ; 127:4, s. 1151-1161 Journal article (peer-reviewed)abstract Perturbations AT of a selfadjoint operator A by symmetric finite rank operators T from H2A) to H-2(A) are studied. The finite dimensional family of selfadjoint extensions determined by AT is given explicitly.
6.	Albeverio, Sergio, et al. (author) Gauge fields, point interactions and few-body problems in one dimension 2004 In: Reports on Mathematical Physics. - 0034-4877. ; 53:3, s. 363-370 Journal article (peer-reviewed)abstract Point interactions for the second derivative operator in one dimension are studied. Every operator from this family is described by the boundary conditions which include a 2 x 2 real matrix with the unit determinant and a phase. The role of the phase parameter leading to unitarily equivalent operators is discussed in the present paper. In particular, it is shown that the phase parameter is not redundant (contrary to previous studios) if nonstationary problems are concerned. It is proven that the phase parameter can be interpreted as the amplitude of a singular gauge field. Considering the few-body problem we extend the range of parameters for which the exact solution can be found using the Bethe Ansatz.
7.	Albeverio, S., et al. (author) Many body problems with "spin"-related contact interactions 2001 In: Reports on mathematical physics. - 0034-4877 .- 1879-0674. ; 47:2, s. 157-166 Journal article (peer-reviewed)abstract We study quantum mechanical systems with "spin"-related contact interactions in one dimension. The boundary conditions describing the contact interactions are dependent on the spin states of the particles. In particular we investigate the integrability of N-body systems with δ-interactions and point spin couplings. Bethe ansatz solutions, bound states and scattering matrices are explicitly given. The cases of generalized separated boundary condition and some Hamiltonian operators corresponding to special spin related boundary conditions are also discussed.
8.	Albeverio, Sergio, et al. (author) On Integrability of Many-Body Problems with Point Interactions 2002 In: Operator Theory: Advances and Applications. ; 132, s. 67-76 Conference paper (peer-reviewed)
9.	Albeverio, S, et al. (author) Point interactions: PT-Hermiticity and reality of the spectrum 2002 In: Letters in Mathematical Physics. - 0377-9017. ; 59:3, s. 227-242 Journal article (peer-reviewed)abstract General point interactions for the second derivative operator in one dimension are studied. In particular, cal PT-self-adjoint point interactions with the support at the origin and at points +/-l are considered. The spectrum of such non-Hermitian operators is investigated and conditions when the spectrum is pure real are presented. The results are compared with those for standard self-adjoint point interactions.
10.	Albeverio, S., et al. (author) Rank one perturbations of not semibounded operators 1997 In: Integral equations and operator theory. - 0378-620X .- 1420-8989. ; 27:4, s. 379-400 Journal article (peer-reviewed)abstract Rank one perturbations of selfadjoint operators which are not necessarily semibounded are studied in the present paper. It is proven that such perturbations are uniquely defined, if they are bounded in the sense of forms. We also show that form unbounded rank one perturbations can be uniquely defined if the original operator and the perturbation are homogeneous with respect to a certain one parameter semigroup. The perturbed operator is defined using the extension theory for symmetric operators. The resolvent of the perturbed operator is calculated using Krein's formula. It is proven that every rank one perturbation can be approximated in the operator norm. We prove that some form unbounded perturbations can be approximated in the strong resolvent sense without renormalization of the coupling constant only if the original operator is not semibounded. The present approach is applied to study first derivative and Dirac operators with point interaction, in one dimension
11.	Albeverio, S., et al. (author) S-matrix, resonances, and wave functions for transport through billiards with leads 1996 In: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 37:10, s. 4888-4903 Journal article (peer-reviewed)abstract For a simple model describing the S-matrices of open resonators the statistical properties of the resonances are investigated, as well as the wave functions inside the resonator
12.	Albeverio, Sergio, et al. (author) Singular cluster interactions in few-body problems 2001 In: Lecture Notes in Pure and Appl. Math.. ; 215, s. 277-292 Conference paper (peer-reviewed)
13.	Albeverio, Sergio, et al. (author) Singular Perturbations of Differential Operators 2000 Book (other academic/artistic)abstract Singular perturbations of Schrödinger type operators are of interest in mathematics, e.g. to study spectral phenomena, and in applications of mathematics in various sciences, e.g. in physics, chemistry, biology, and in technology. They also often lead to models in quantum theory which are solvable in the sense that the spectral characteristics (eigenvalues, eigenfunctions, and scattering matrix) can be computed. Such models then allow us to grasp the essential features of interesting and complicated phenomena and serve as an orientation in handling more realistic situations. In the last ten years two books have appeared on solvable models in quantum theory built using special singular perturbations of Schrödinger operators. The book by S. Albeverio, F. Gesztesy, R. Hoegh-Krohn and H. Holden "Solvable Models in Quantum Mechanics" describes the models in rigorous mathematical terms. It gives a detailed analysis of perturbations of the Laplacian in R^d, d=1,2,3, by potentials with support on a discrete finite or infinite set of point sources (chosen in a deterministic, respectively, stochastic manner). Physically these operators describe the motion of a quantum mechanical particle moving under the action of a potential supported, e.g., by the points of a crystal lattice or a random solid. Such systems and models are also described in physical terms in the book by Yu.N.Demkov and V.N.Ostrovsky "Zero-range Potentials in Atomic Physics", which also contains a description of applications in other areas such as in optics and electromagnetism. Let us also remark that a translation of the book by S.Albeverio, F.Gesztesy, R.Hoegh-Krohn and H.Holden in Russian has been published with additional comments and literature. Since the appearance of these books several important new developments have taken place. It is the main aim of the present book to present some of these new developments in a unified formalism which also puts some of the basic results of the preceding books into a new light. The new developments concern in particular a systematic study of finite rank perturbations of (self--adjoint) operators (in particular differential operators), of generalized (singular) perturbations, of the corresponding scattering theory as well as infinite rank perturbations and multiple particles (many--body) problems in quantum theory. We also present the theory of point interaction Hamiltonians, as a particular case of a general theory of singular perturbations of differential operators. This theory has received steadily increasing attention over the years also for its many applications in physics (solid state physics, nuclear physics), electromagnetism (antennas), and technology (metallurgy, nanophysics). We hope this monograph can serve as a basis for orientation in a rapidly developing area of analysis, mathematical physics and their applications.
14.	Albeverio, Sergio, et al. (author) Singular perturbations of differential operators : solvable Schrödinger type operators 2000 Book (peer-reviewed)
15.	Albeverio, S., et al. (author) Symmetries of Schrödinger operator with point interactions 1998 In: Letters in Mathematical Physics. - 0377-9017 .- 1573-0530. ; 45, s. 33-47 Journal article (peer-reviewed)abstract The transformations of all the Schrödinger operators with point interactions in dimension one under space reflection P, time reversal T and (Weyl) scaling Wλ are presented. In particular, those operators which are invariant (possibly up to a scale) are selected. Some recent papers on related topics are commented upon
16.	Astudillo, Maria, et al. (author) RJ -Symmetric Laplace Operators on Star Graphs : Real Spectrum and Self-Adjointness 2015 In: Advances in Mathematical Physics. - : Hindawi Limited. - 1687-9120 .- 1687-9139. Journal article (peer-reviewed)abstract How ideas of PJ -symmetric quantum mechanics can be applied to quantum graphs is analyzed, in particular to the star graph. The class of rotationally symmetric vertex conditions is analyzed. It is shown that all such conditions can effectively be described by circulantmatrices: real in the case of odd number of edges and complex having particular block structure in the even case. Spectral properties of the corresponding operators are discussed.
17.	Astudillo, Maria, et al. (author) RT-symmetric Laplace operators on star graphs : real spectrum and self-adjointness 2015 Reports (other academic/artistic)abstract In the current article it is analyzed how ideas of PT-symmetricquantum mechanics can be applied to quantum graphs, in particular tothe star graph. The class of rotationally-symmetric vertex conditionsis analyzed. It is shown that all such conditions can effectively be described bycirculant matrices: real in the case of odd number of edges and complex having particular block structure in the even case. Spectral properties of thecorresponding operators are discussed.
18.	Avdonin, Sergei, et al. (author) Inverse problems for quantum trees 2008 In: INVERSE PROBLEMS AND IMAGING. - 1930-8337 .- 1930-8345. ; 2:1, s. 1-21 Journal article (peer-reviewed)abstract Three different inverse problems for the Schrodinger operator on a metric tree are considered, so far with standard boundary conditions at the vertices. These inverse problems are connected with the matrix Titchmarsh-Weyl function, response operator ( dynamic Dirichlet-to-Neumann map) and scattering matrix. Our approach is based on the boundary control ( BC) method and in particular on the study of the response operator. It is proven that the response operator determines the quantum tree completely, i.e. its connectivity, lengths of the edges and potentials on them. The same holds if the response operator is known for all but one boundary points, as well as for the Titchmarsh-Weyl function and scattering matrix. If the connectivity of the graph is known, then the lengths of the edges and the corresponding potentials are determined by just the diagonal terms of the data.
19.	Avdonin, Sergei, et al. (author) INVERSE PROBLEMS FOR QUANTUM TREES II : RECOVERING MATCHING CONDITIONS FOR STAR GRAPHS 2010 In: Inverse Problems and Imaging. - : American Institute of Mathematical Sciences (AIMS). - 1930-8337 .- 1930-8345. ; 4:4, s. 579-598 Journal article (peer-reviewed)abstract The inverse problem for the Schrodinger operator on a star graph is investigated. It is proven that such Schrodinger operator, i.e. the graph, the real potential on it and the matching conditions at the central vertex, can be reconstructed from the Titchmarsh-Weyl matrix function associated with the graph boundary. The reconstruction is also unique if the spectral data include not the whole Titchmarsh-Weyl function but its principal block (the matrix reduced by one dimension). The same result holds true if instead of the Titchmarsh-Weyl function the dynamical response operator or just its principal block is known.
20.	Bauch, S., et al. (author) Some Applications of Generalized Euler Characteristic of Quantum Graphs and Microwave Networks 2021 In: Acta Physica Polonica. A. - 0587-4246 .- 1898-794X. ; 140:6, s. 525-531 Journal article (peer-reviewed)abstract In this article we continue to explore the possibilities offered by our discovery that one of the main graph and network characteristic, the generalized Euler characteristic iG, can be determined from a graph/network spectrum. We show that using the generalized Euler characteristic iG the number of vertices with Dirichlet \|VD\| boundary conditions of a family of graphs/networks created on the basis of the standard quantum graphs or microwave networks can be easily identified. We also present a new application of the generalized Euler characteristic for checking the completeness of graphs/networks spectra in the low energy range.
21.	Berkolaiko, Gregory, et al. (author) Edge connectivity and the spectral gap of combinatorial and quantum graphs 2017 In: Journal of Physics A. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 50:36 Journal article (peer-reviewed)abstract We derive a number of upper and lower bounds for the first nontrivial eigenvalue of Laplacians on combinatorial and quantum graph in terms of the edge connectivity, i.e. the minimal number of edges which need to be removed to make the graph disconnected. On combinatorial graphs, one of the bounds corresponds to a well-known inequality of Fiedler, of which we give a new variational proof. On quantum graphs, the corresponding bound generalizes a recent result of Band and Levy. All proofs are general enough to yield corresponding estimates for the p-Laplacian and allow us to identify the minimizers. Based on the Betti number of the graph, we also derive upper and lower bounds on all eigenvalues which are 'asymptotically correct', i.e. agree with the Weyl asymptotics for the eigenvalues of the quantum graph. In particular, the lower bounds improve the bounds of Friedlander on any given graph for all but finitely many eigenvalues, while the upper bounds improve recent results of Ariturk. Our estimates are also used to derive bounds on the eigenvalues of the normalized Laplacian matrix that improve known bounds of spectral graph theory.
22.	Berkolaiko, Gregory, et al. (author) Impediments to diffusion in quantum graphs : Geometry-based upper bounds on the spectral gap 2023 In: Proceedings of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9939 .- 1088-6826. ; 151, s. 3439-3455 Journal article (peer-reviewed)abstract We derive several upper bounds on the spectral gap of the Laplacian on compact metric graphs with standard or Dirichlet vertex conditions. In particular, we obtain estimates based on the length of a shortest cycle (girth), diameter, total length of the graph, as well as further metric quantities introduced here for the first time, such as the avoidance diameter. Using known results about Ramanujan graphs, a class of expander graphs, we also prove that some of these metric quantities, or combinations thereof, do not to deliver any spectral bounds with the correct scaling.
23.	Berkolaiko, Gregory, et al. (author) SURGERY PRINCIPLES FOR THE SPECTRAL ANALYSIS OF QUANTUM GRAPHS 2019 In: Transactions of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9947 .- 1088-6850. ; 372:7, s. 5153-5197 Journal article (peer-reviewed)abstract We present a systematic collection of spectral surgery principles for the Laplacian on a compact metric graph with any of the usual vertex conditions (natural, Dirichlet, or delta-type) which show how various types of changes of a local or localised nature to a graph impact on the spectrum of the Laplacian. Many of these principles are entirely new; these include transplantation of volume within a graph based on the behaviour of its eigenfunctions, as well as unfolding of local cycles and pendants. In other cases we establish sharp generalisations, extensions, and refinements of known eigenvalue inequalities resulting from graph modification, such as vertex gluing, adjustment of vertex conditions, and introducing new pendant subgraphs. To illustrate our techniques we derive a new eigenvalue estimate which uses the size of the doubly connected part of a compact metric graph to estimate the lowest non-trivial eigenvalue of the Laplacian with natural vertex conditions. This quantitative isoperimetric-type inequality interpolates between two known estimates - one assuming the entire graph is doubly connected and the other making no connectivity assumption (and producing a weaker bound) - and includes them as special cases.
24.	Boman, Jan, et al. (author) Schrödinger Operators on Graphs and Geometry II. Integrable Potentials and an Ambartsumian Theorem 2016 Reports (other academic/artistic)
25.	Boman, Jan, et al. (author) Schrödinger Operators on Graphs and Geometry II. Spectral Estimates for L-1-potentials and an Ambartsumian Theorem 2018 In: Integral equations and operator theory. - : Springer Science and Business Media LLC. - 0378-620X .- 1420-8989. ; 90:3 Journal article (peer-reviewed)abstract In this paper we study Schrodinger operators with absolutely integrable potentials on metric graphs. Uniform bounds-i.e. depending only on the graph and the potential-on the difference between the eigenvalues of the Laplace and Schrodinger operators are obtained. This in turn allows us to prove an extension of the classical Ambartsumian Theorem which was originally proven for Schrodinger operators with Neumann conditions on an interval. We also extend a previous result relating the spectrum of a Schrodinger operator to the Euler characteristic of the underlying metric graph.
26.	Boman, J, et al. (author) Symmetries of quantum graphs and the inverse scattering problem 2005 In: Advances in Applied Mathematics. - : Elsevier BV. - 1090-2074 .- 0196-8858. ; 35:1, s. 58-70 Journal article (peer-reviewed)abstract The Schrodinger equation on a graph together with a set of self-adjoint boundary conditions at the vertices determine a quantum graph. If the graph has one or more infinite edges one can associate a scattering matrix to the quantum graph. It is proved that if such a graph has internal symmetries then the boundary conditions, and hence the self-adjoint operator describing the quantum system, in general cannot be reconstructed from the scattering matrix. In addition it is shown that if the Schrodinger operator possesses internal symmetry then there exists a different quantum graph associated with the same scattering matrix.
27.	Carlehed, Magnus, et al. (author) Mikael passare 2017 In: Analysis Meets Geometry. Trends in Mathematics. Andersson M., Boman J., Kiselman C., Kurasov P., Sigurdsson R. (eds). - Cham : Springer. - 2297-0215 .- 2297-024X. - 9783319524719 - 9783319524696 ; , s. 59-60 Book chapter (other academic/artistic)abstract I got to know Mikael in the eighties, when I was a PhD student at Stockholm University. I had completed a number of graduate courses and became interested in complex analysis. Mikael was a young lecturer in Stockholm, and our overlapping interest in that subject brought us into each other’s orbits.
28.	Dijksma, A, et al. (author) High order singular rank one perturbations of a positive operator 2005 In: Integral Equations and Operator Theory. - : Springer Science and Business Media LLC. - 1420-8989 .- 0378-620X. ; 53:2, s. 209-245 Journal article (peer-reviewed)abstract In this paper self-adjoint realizations in Hilbert and Pontryagin spaces of the formal expression L-alpha = L + <(.),psi >psi are discussed and compared. Here L is a positive self-adjoint operator in a Hilbert space H with inner product <(.), (.)>, a is a real parameter, and p in the rank one perturbation is a singular element belonging to H-nH-n+1 with n >= 3, where {H-s}(s=-infinity)(infinity) is the scale of Hilbert spaces associated with L in H.
29.	Elander, Nils, et al. (author) Complex scaling and self adjoint dilations 1993 In: International Journal of Quantum Chemistry. - : Wiley. - 0020-7608 .- 1097-461X. ; 46:3, s. 415-418 Journal article (peer-reviewed)abstract Complex scaling of the Schrodinger equation on the halfaxis with a nontrivial boundary condition at the origin is investigated. A self-adjoint dilation of the corresponding dissipative operator is constructed. The relations between the scattering problems for the operator and it's dilation are clarified
30.	Janas, Jan, et al. (author) Methods of spectral analysis in mathematical physics 2009 In: Operator Theory: Advances and Applications. - 0255-0156. ; 186 Journal article (peer-reviewed)
31.	Karreskog, Gustav, et al. (author) SCHRODINGER OPERATORS ON GRAPHS : SYMMETRIZATION AND EULERIAN CYCLES 2016 In: Proceedings of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9939 .- 1088-6826. ; 144:3, s. 1197-1207 Journal article (peer-reviewed)abstract Spectral properties of the Schrodinger operator on a finite compact metric graph with delta-type vertex conditions are discussed. Explicit estimates for the lowest eigenvalue (ground state) are obtained using two different methods: Eulerian cycle and symmetrization techniques.
32.	Karreskog, Gustav, 1991-, et al. (author) Schrödinger operators on graphs : symmetrization and Eulerian cycles 2015 Reports (other academic/artistic)abstract Spectral properties of the Schrödinger operator on a finite compact metric graph with delta-type vertex conditions are discussed. Explicit estimates for the lowest eigenvalue (ground state) are obtained using two different methods:Eulerian cycle and symmetrization techniques. In the case of positive interactions even estimates for higher eigenvalues are derived.
33.	Kennedy, James B., et al. (author) A theory of spectral partitions of metric graphs 2021 In: Calculus of Variations and Partial Differential Equations. - : Springer Science and Business Media LLC. - 0944-2669 .- 1432-0835. ; 60:2 Journal article (peer-reviewed)abstract We introduce an abstract framework for the study of clustering in metric graphs: after suitably metrising the space of graph partitions, we restrict Laplacians to the clusters thus arising and use their spectral gaps to define several notions of partition energies; this is the graph counterpart of the well-known theory of spectral minimal partitions on planar domains and includes the setting in Band et al. (Commun Math Phys 311:815-838, 2012) as a special case. We focus on the existence of optimisers for a large class of functionals defined on such partitions, but also study their qualitative properties, including stability, regularity, and parameter dependence. We also discuss in detail their interplay with the theory of nodal partitions. Unlike in the case of domains, the one-dimensional setting of metric graphs allows for explicit computation and analytic-rather than numerical-results. Not only do we recover the main assertions in the theory of spectral minimal partitions on domains, as studied in Conti et al. (Calc Var 22:45-72, 2005), Helffer et al. (Ann Inst Henri Poincare Anal Non Lineaire 26:101-138, 2009), but we can also generalise some of them and answer (the graph counterparts of) a few open questions.
34.	Kennedy, J. B., et al. (author) On the Spectral Gap of a Quantum Graph 2016 In: Annales de l'Institute Henri Poincare. Physique theorique. - : Birkhauser Verlag AG. - 1424-0637 .- 1424-0661. ; , s. 1-35 Journal article (peer-reviewed)abstract We consider the problem of finding universal bounds of “isoperimetric” or “isodiametric” type on the spectral gap of the Laplacian on a metric graph with natural boundary conditions at the vertices, in terms of various analytical and combinatorial properties of the graph: its total length, diameter, number of vertices and number of edges. We investigate which combinations of parameters are necessary to obtain non-trivial upper and lower bounds and obtain a number of sharp estimates in terms of these parameters. We also show that, in contrast to the Laplacian matrix on a combinatorial graph, no bound depending only on the diameter is possible. As a special case of our results on metric graphs, we deduce estimates for the normalised Laplacian matrix on combinatorial graphs which, surprisingly, are sometimes sharper than the ones obtained by purely combinatorial methods in the graph theoretical literature.
35.	Kennedy, James B., et al. (author) On the spectral gap of a quantum graph 2015 Reports (other academic/artistic)abstract We consider the problem of finding universal bounds of “isoperimetric” or “isodiametric” type on the spectral gap of the Laplacian on a metric graph with natural boundary conditions at the vertices, in terms of various analytical and combinatorial properties of the graph: its total length, diameter, number of vertices and number of edges. We investigate which combinations of parameters are necessary to obtain non-trivial upper and lower bounds and obtain a number of sharp estimates in terms of these parameters. We also show that, in contrast to the Laplacian matrix on a combinatorial graph, no bound depending only on the diameter is possible. As a special case of our results on metric graphs, we deduce estimates for the normalised Laplacian matrix on combinatorial graphs which, surprisingly, are sometimes sharper than the ones obtained by purely combinatorial methods in the graph theoretical literature.
36.	Kiik, Jean-Claude, et al. (author) On vertex conditions for elastic systems 2015 In: Physics Letters A. - Stockholm : Department of Mathematics, Stockholm University. - 0375-9601 .- 1873-2429. ; 379:34-35, s. 1871-1876 Reports (other academic/artistic)abstract In this paper vertex conditions for the fourth order differential operator on the simplest metric graph - the $ Y$-graph, -are discussed. In order to make the operator symmetric one needs to impose extra conditions on the limit values offunctions and their derivatives at the central vertex. It is shown that such conditions corresponding to the free movement of beams depend on the angles between the beams in the equilibrium position.
37.	Kuperin, Yuri, et al. (author) Connexions and Effective S-matrix in Triangle Representation for Quantum Scattering 1991 In: Annals of Physics. - : Elsevier BV. - 0003-4916. ; 205:2, s. 330-361 Journal article (peer-reviewed)abstract For quantum few-body systems, a method of spectral representation generated by specially extracted sub-Hamiltonians is developed. In this approach, the connections between the geometry of a base manifold, the spectral structure of sub-Hamiltonians, and the geometric characteristics of induced Hilbert bundles are investigated. The appropriate relations between connections on these Hilbert bundles and global invariants of S-matrix are obtained. Some applications of the proposed approach to exactly solvable two- and three-body scattering problems are considered.
38.	Kurasov, Pavel (author) A one-electron model of a Long Molecule 1989 In: Leningrad university vesting. ; 3:18, s. 8-15 Journal article (peer-reviewed)
39.	Kurasov, Pavel, et al. (author) AHARONOV-BOHM RING TOUCHING A QUANTUM WIRE : HOW TO MODEL IT AND TO SOLVE THE INVERSE PROBLEM 2011 In: Reports on mathematical physics. - 0034-4877 .- 1879-0674. ; 68:3, s. 271-287 Journal article (peer-reviewed)abstract An explicitly solvable model of the gated Aharonov-Bohm ring touching a quantum wire is constructed and investigated. The inverse spectral and scattering problems are discussed. It is shown that the Titchmarsh-Weyl matrix function associated with the boundary vertices determines a unique electric potential on the graph even though the graph contains a loop. This system gives another family of isospectral quantum graphs.
40.	Kurasov, Pavel, 1964- (author) Always Detectable Eigenfunctions on Metric Graphs 2021 In: Acta Physica Polonica. A. - 0587-4246 .- 1898-794X. ; 140:6, s. 510-513 Journal article (peer-reviewed)abstract It is proven that Laplacians with standard vertex continuous on metric trees and with standard and Dirichlet conditions on arbitrary metric graphs possess an infinite sequence of simple eigenvalues with the eigenfunctions not equal to zero in any non-Dirichlet vertex.
41.	Kurasov, Pavel, et al. (author) An electron in a Homogeneous Crystal of Point Atoms with Internal Structure II 1988 In: Theoretical and Mathematical Physics. - 0040-5779. ; 74:1, s. 82-93 Journal article (peer-reviewed)abstract A spectral analysis is made of a Schrodinger operator with zero-range potential of a one- or two-dimensional lattice in the resonances of an isolated atom and the spectral properties of the crystal is established
42.	Kurasov, Pavel, 1964-, et al. (author) An electron in a Homogeneous Crystal of Point Atoms with Internal Structure II 1988 In: Advances in Theoretical and Mathematical Physics. - 1095-0761 .- 1095-0753. Journal article (peer-reviewed)
43.	Kurasov, Pavel, et al. (author) An Operator Theoretic Interpretation of the Generalized Titchmarsh-Weyl Coefficient for a Singular Sturm-Liouville Problem 2011 In: Mathematical physics, analysis and geometry. - : Springer Science and Business Media LLC. - 1385-0172 .- 1572-9656. ; 14:2, s. 115-151 Journal article (peer-reviewed)abstract In this article an operator theoretic interpretation of the generalized Titchmarsh-Weyl coefficient for the Hydrogen atom differential expression is given. As a consequence we obtain a new expansion theorem in terms of singular generalized eigenfunctions.
44.	Kurasov, Pavel, et al. (author) Analytic solutions for stochastic hybrid models of gene regulatory networks 2021 In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 82:1-2 Journal article (peer-reviewed)abstract Discrete-state stochastic models are a popular approach to describe the inherent stochasticity of gene expression in single cells. The analysis of such models is hindered by the fact that the underlying discrete state space is extremely large. Therefore hybrid models, in which protein counts are replaced by average protein concentrations, have become a popular alternative. The evolution of the corresponding probability density functions is given by a coupled system of hyperbolic PDEs. This system has Markovian nature but its hyperbolic structure makes it difficult to apply standard functional analytical methods. We are able to prove convergence towards the stationary solution and determine such equilibrium explicitly by combining abstract methods from the theory of positive operators and elementary ideas from potential analysis.
45.	Kurasov, Pavel, et al. (author) Asymptotically isospectral quantum graphs and generalised trigonometric polynomials 2020 In: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 488:1 Journal article (peer-reviewed)abstract The theory of almost periodic functions is used to investigate spectral properties of Schrodinger operators on metric graphs, also known as quantum graphs. In particular we prove that two Schrodinger operators may have asymptotically close spectra if and only if the corresponding reference Laplacians are isospectral. Our result implies that a Schrodinger operator is isospectral to the standard Laplacian on a may be different metric graph only if the potential is identically equal to zero.
46.	Kurasov, Pavel, et al. (author) ASYMPTOTICALLY ISOSPECTRAL QUANTUM GRAPHS AND TRIGONOMETRIC POLYNOMIALS 2018 Reports (other academic/artistic)abstract The theory of almost periodic functions is used to investigate spectral properties of Schrödinger operators on metric graphs, also known as quantum graphs. In particular we prove that two Schrödinger operators may have asymptotically close spectra if and only if the corresponding Laplacians are isospectral. The case of general vertex conditions and integrable potentials is considered. In particular, our result implies that a Schrödinger operator is isospectral to the standard Laplacian on a may be different metric graph only if the potential is identically equal to zero.
47.	Kurasov, Pavel B., 1964- (author) On direct and inverse scattering problems in dimension one 1993 Doctoral thesis (other academic/artistic)abstract Direct and inverse scattering problems for the Schrödinger operator in dimension one are investigated. Relations between the scattering problems defined by regular and zero range potentials are investigated.Correct mathematical definition of the «^'-interaction is introduced and investigated in detail. Relations with the complex scaling procedure are analyzed. The inverse scattering problem for long range oscillating potentials is investigated. Nonuniqueness of the solution of this problem is observed. It leads to a new soliton like solution of the KdV equation. Potentials, corresponding to the same scattering matrix as certain zero range potentials, are calculated. A model scattering theory for three one dimensional particles is constructed using the theory of selfadjoint extensions for symmetric operators. The scattering matrix is calculated in terms of elementary functions. Decay operators are introduced for the Schrödinger evolution in the framework of the Lax-Phillips scattering theory.
48.	Kurasov, Pavel (author) Can One Distinguish Quantum Trees From The Boundary? 2012 In: Proceedings of the American Mathematical Society. - 1088-6826 .- 0002-9939. ; 140:7, s. 2347-2356 Journal article (peer-reviewed)abstract Schrodinger operators on metric trees are considered. It is proven that for certain matching conditions the Titchmarsh-Weyl matrix function does not determine the underlying metric tree; i.e. there exist quantum trees with equal Titchmarsh-Weyl functions. The constructed trees form one-parameter families of isospectral and isoscattering graphs.
49.	Kurasov, Pavel, et al. (author) Cluster Resonances and Bound States and Crystal Band Spectrum 1991 In: NATO ASI Series. ; , s. 617-622 Conference paper (peer-reviewed)
50.	Kurasov, Pavel, 1964-, et al. (author) Connexions and Effective S-matrix in Triangle Representation for Quantum Scattering 1991 In: Annals of Physics. - 0003-4916 .- 1096-035X. Journal article (peer-reviewed)

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