Results 1 - 10 of 2217
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[en] Let Mn be an n×n real (resp. complex) Wigner matrix and UnΛnUn* be its spectral decomposition. Set (y1,y2⋯,yn)T=Un*x, where x = (x1, x2, ⋅⋅⋅, xn)T is a real (resp. complex) unit vector. Under the assumption that the elements of Mn have 4 matching moments with those of GOE (resp. GUE), we show that the process Xn(t)=√((βn)/2 )∑i=1⌊nt⌋(|yi|2−1/n ) converges weakly to the Brownian bridge for any x satisfying ‖x‖∞ → 0 as n → ∞, where β = 1 for the real case and β = 2 for the complex case. Such a result indicates that the orthogonal (resp. unitary) matrices with columns being the eigenvectors of Wigner matrices are asymptotically Haar distributed on the orthogonal (resp. unitary) group from a certain perspective
[en] The higher-derivative theories with degenerate frequencies exhibit BRST symmetry [V.O. Rivelles, Phys. Lett. B 577 (2003) 147]. In the present Letter meaning of BRST-invariance condition is analyzed. The BRST symmetry is related to nondiagonalizability of the Hamiltonian and it is shown that BRST condition singles out the subspace spanned by proper eigenvectors of the Hamiltonian.
[en] Some computational methods for the evaluation of eigenvalues and eigenvectors of (square) real matrices are briefly described. The methods of Jacobi, Given and Householder are used for real-symmetric matrices while Lanczos's method, supertriangularization and deflation methods are used for real-non symmetric matrices. (author)
[en] Quark propagators are constructed in the external non-Abelian fields of chromium-magnetic type. A notable difference in guark propagators for chromomagnetic field determined by various types of potentials is shown. Quark spectrum continuity appears to be a norable feature of constant non-Abelian fields
[en] We propose the use of quasars with accretion rate near the Eddington ratio (extreme quasars) as standard candles. The selection criteria are based on the Eigenvector 1 (E1) formalism. Our first sample is a selection of 334 optical quasar spectra from the SDSS DR7 database with a S/N > 20. Using the E1, we define primary and secondary selection criteria in the optical spectral range. We show that it is possible to derive a redshift-independent estimate of luminosity for extreme Eddington ratio sources. Our results are consistent with concordance cosmology but we need to work with other spectral ranges to take into account the quasar orientation, among other constrains.
[en] We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, we give conditions under which these Hamiltonians can be factorized in terms of generalized lowering and raising operators
[en] We have recently proposed a strategy to produce, starting from a given Hamiltonian h1 and a certain operator x for which [h1,xx†]=0 and x†x is invertible, a second Hamiltonian h2 with the same eigenvalues as h1 and whose eigenvectors are related to those of h1 by x†. Here we extend this procedure to build up a second Hamiltonian, whose eigenvalues are different from those of h1, and whose eigenvectors are still related as before. This new procedure is also extended to crypto-hermitian Hamiltonians. -- Highlights: ► Given two operators (h,x) we define H whose eigensystem is deduced from that of h. ► We extend this procedure to a crypto-hermitian Hamiltonians. ► We discuss the role of intertwining operators, bounded or not, in this construction.
[en] A new algorithm for simultaneous coordinate relaxation is described. For the determination of several extreme eigenvalues and eigenvectors of large, sparse matrices the simultaneous algorithm affords significant advantages in comparison with a coordinate relaxation algorithm applied to determine individual eigenvalues and eigenvectors in turn. Results of application of the algorithm to test matrices are discussed
[en] Using large arguments, we propose a scheme for calculating the two-point eigenvector correlation function for non-normal random matrices in the large limit. The setting generalizes the quaternionic extension of free probability to two-point functions. In the particular case of biunitarily invariant random matrices, we obtain a simple, general expression for the two-point eigenvector correlation function, which can be viewed as a further generalization of the single ring theorem. This construction has some striking similarities to the freeness of the second kind known for the Hermitian ensembles in large . On the basis of several solved examples, we conjecture two kinds of microscopic universality of the eigenvectors — one in the bulk, and one at the rim. The form of the conjectured bulk universality agrees with the scaling limit found by Chalker and Mehlig [JT Chalker, B Mehlig, Phys. Rev. Lett. 81 (1998) 3367] in the case of the complex Ginibre ensemble.