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On the Law of Addition of Random Matrices
 COMMUNICATIONS IN MATHEMATICAL PHYSICS
, 2000
"... Normalized eigenvalue counting measure of the sum of two Hermitian (or real symmetric) matrices An and Bn rotated independently with respect to each other by the random unitary (or orthogonal) Haar distributed matrix Un (i.e. An + U ∗ n BnUn) is studied in the limit of large matrix order n. Converg ..."
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Normalized eigenvalue counting measure of the sum of two Hermitian (or real symmetric) matrices An and Bn rotated independently with respect to each other by the random unitary (or orthogonal) Haar distributed matrix Un (i.e. An + U ∗ n BnUn) is studied in the limit of large matrix order n. Convergence in probability to a limiting nonrandom measure is established. A functional equation for the Stieltjes transform of the limiting measure in terms of limiting eigenvalue measures of An and Bn is obtained and studied.
Symmetry, Integrability and Geometry: Methods and Applications On the Spectrum of a Discrete NonHermitian Quantum System ⋆
"... Abstract. In this paper, we develop spectral analysis of a discrete nonHermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple conditions for discreteness of the spectrum are established. Key words: difference operator; ..."
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Abstract. In this paper, we develop spectral analysis of a discrete nonHermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple conditions for discreteness of the spectrum are established. Key words: difference operator; nonHermiticity; spectrum; eigenvalue; eigenvector; completely continuous operator 2000 Mathematics Subject Classification: 39A70; 81Q10 1
Symmetry, Integrability and Geometry: Methods and Applications Harmonic Analysis on Quantum Complex Hyperbolic Spaces ⋆
"... Abstract. In this paper we obtain some results of harmonic analysis on quantum complex hyperbolic spaces. We introduce a quantum analog for the Laplace–Beltrami operator and its radial part. The latter appear to be second order qdifference operator, whose eigenfunctions are related to the AlSalam– ..."
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Abstract. In this paper we obtain some results of harmonic analysis on quantum complex hyperbolic spaces. We introduce a quantum analog for the Laplace–Beltrami operator and its radial part. The latter appear to be second order qdifference operator, whose eigenfunctions are related to the AlSalam–Chihara polynomials. We prove a Plancherel type theorem for it. Key words: quantum groups, harmonic analysis on quantum symmetric spaces; qdifference operators; AlSalam–Chihara polynomials; Plancherel formula 2010 Mathematics Subject Classification: 17B37; 20G42; 81R50; 33D45; 42C10 1
Singular Potentials in Quantum Mechanics and Ambiguity in the SelfAdjoint Hamiltonian
, 2007
"... For a class of singular potentials, including the Coulomb potential (in three and less dimensions) and V (x) = g/x2 with the coefficient g in a certain range (x being a space coordinate in one or more dimensions), the corresponding Schrödinger operator is not automatically selfadjoint on its natur ..."
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For a class of singular potentials, including the Coulomb potential (in three and less dimensions) and V (x) = g/x2 with the coefficient g in a certain range (x being a space coordinate in one or more dimensions), the corresponding Schrödinger operator is not automatically selfadjoint on its natural domain. Such operators admit more than one selfadjoint domain, and the spectrum and all physical consequences depend seriously on the selfadjoint version chosen. The article discusses how the selfadjoint domains can be identified in terms of a boundary condition for the asymptotic behaviour of the wave functions around the singularity, and what physical differences emerge for different selfadjoint versions of the Hamiltonian. The paper reviews and interprets known results, with the intention to provide a practical guide for all those interested in how to approach these ambiguous situations.
Singular Potentials in Quantum Mechanics and Ambiguity in the SelfAdjoint Hamiltonian ⋆
, 708
"... Abstract. For a class of singular potentials, including the Coulomb potential (in three and less dimensions) and V (x) = g/x 2 with the coefficient g in a certain range (x being a space coordinate in one or more dimensions), the corresponding Schrödinger operator is not automatically selfadjoint o ..."
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Abstract. For a class of singular potentials, including the Coulomb potential (in three and less dimensions) and V (x) = g/x 2 with the coefficient g in a certain range (x being a space coordinate in one or more dimensions), the corresponding Schrödinger operator is not automatically selfadjoint on its natural domain. Such operators admit more than one selfadjoint domain, and the spectrum and all physical consequences depend seriously on the selfadjoint version chosen. The article discusses how the selfadjoint domains can be identified in terms of a boundary condition for the asymptotic behaviour of the wave functions around the singularity, and what physical differences emerge for different selfadjoint versions of the Hamiltonian. The paper reviews and interprets known results, with the intention to provide a practical guide for all those interested in how to approach these ambiguous situations.
ABSENCE OF NORMALIZABLE TIMEPERIODIC SOLUTIONS FOR THE DIRAC EQUATION IN KERRNEWMANDS BLACK HOLE BACKGROUND
, 807
"... Abstract. We consider the Dirac equation on the background of a KerrNewmande Sitter black hole. By performing variable separation, we show that there exists no timeperiodic and normalizable solution of the Dirac equation. This conclusion holds true even in the extremal case. With respect to previ ..."
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Abstract. We consider the Dirac equation on the background of a KerrNewmande Sitter black hole. By performing variable separation, we show that there exists no timeperiodic and normalizable solution of the Dirac equation. This conclusion holds true even in the extremal case. With respect to previously considered cases, the novelty is represented by the presence, together with a black hole event horizon, of a cosmological (non degenerate) event horizon, which is at the root of the possibility to draw a conclusion on the aforementioned topic in a straightforward way even in the extremal case. 1.
ftp (login: ftp) 147.26.103.110 or 129.120.3.113 The Schrödinger equation on
"... nonstationary domains ∗ ..."