| 1. |
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| 2. |
- Kurasov, Pavel, et al.
(author)
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Surfaces with an Internal Structure
- 1989
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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
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Conference paper (peer-reviewed)
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| 3. |
- Kurasov, Pavel, et al.
(author)
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Three One-dimensional Bosons with an Internal Structure
- 1988
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In: Schrödinger operators, standard and nonstandard. - 9971508400 ; , s. 166-188
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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
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| 4. |
- Albeverino, S., et al.
(author)
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Pseudo-Differential Operators with Point Interactions
- 1997
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In: Letters in Mathematical Physics. - 0377-9017 .- 1573-0530. ; 41, s. 79-92
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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.
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| 5. |
- Albeverio, S., et al.
(author)
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Finite rank perturbations and distribution theory
- 1999
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In: Proceedings of the American Mathematical Society. - 0002-9939 .- 1088-6826. ; 127:4, s. 1151-1161
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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.
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| 6. |
- Albeverio, Sergio, et al.
(author)
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Gauge fields, point interactions and few-body problems in one dimension
- 2004
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In: Reports on Mathematical Physics. - 0034-4877. ; 53:3, s. 363-370
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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.
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| 7. |
- Albeverio, S., et al.
(author)
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Many body problems with "spin"-related contact interactions
- 2001
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In: Reports on mathematical physics. - 0034-4877 .- 1879-0674. ; 47:2, s. 157-166
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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.
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| 8. |
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| 9. |
- Albeverio, S, et al.
(author)
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Point interactions: PT-Hermiticity and reality of the spectrum
- 2002
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In: Letters in Mathematical Physics. - 0377-9017. ; 59:3, s. 227-242
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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.
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| 10. |
- Albeverio, S., et al.
(author)
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Rank one perturbations of not semibounded operators
- 1997
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In: Integral equations and operator theory. - 0378-620X .- 1420-8989. ; 27:4, s. 379-400
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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
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