| 1. |
- 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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| 2. |
- Albeverio, S., et al.
(author)
-
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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| 3. |
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| 4. |
- Albeverio, S., et al.
(author)
-
Operator calculus for p-adic valued symbols and quantization
- 2009
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In: Rendicoti Del Seminario Matematico. - 0373-1243. ; 67:2, s. 137-150
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Journal article (peer-reviewed)abstract
- The aim of this short review is to attract the attention of the pseudo-differentialcommunity to possibilities in the development of operator calculus for symbols (dependingon p-adic conjugate variables) taking values in fields of p-adic numbers. Essentials of thiscalculus were presented in works of the authors of this paper in order to perform p-adic valuedquantization. Unfortunately, this calculus still has not attracted a great deal of attentionfrom pure mathematicians, although it opens new and interesting domains for the theory ofpseudo-differential operators.
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| 5. |
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| 6. |
- Albeverio, S, et al.
(author)
-
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
-
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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| 7. |
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| 8. |
- 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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| 9. |
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| 10. |
- Albeverio, S., et al.
(author)
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Symmetries of Schrödinger operator with point interactions
- 1998
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In: Letters in Mathematical Physics. - 0377-9017 .- 1573-0530. ; 45, s. 33-47
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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
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