Related papers: Hermitian Matrix Diagonalization and its Symmetry …
In this article, we point out that the effective Hamiltonian for neutrino oscillations in matter is invariant under the transformation of the mixing angle $\theta^{}_{12} \to \theta^{}_{12} - \pi/2$ and the exchange of first two neutrino…
We consider a set of N linearly coupled harmonic oscillators and show that the diagonalization of this problem can be put in geometrical terms. The matrix techniques developed here allowed for solutions in both the classical and quantum…
It has been established that a positive semi-definite Hamiltonian,$H$, that has a tridiagonal matrix representation in a basis set, allows a definition of forward (and backward) shift operators that can be used to define the matrix…
It is known that hermitean random matrix ensembles can be identified with symmetric coset spaces of Lie groups, or else with tangent spaces of the same. This results in a classification of random matrix ensembles as well as applications in…
A recursive method is derived to calculate all eigenvalue correlation functions of a random hermitian matrix in the large size limit, and after smoothing of the short scale oscillations. The property that the two-point function is…
We derive the loop equations for the one Hermitian matrix model in any dimension. These are a consequence of the Schwinger-Dyson equations of the model. Moreover we show that in leading order of large $N$ the loop equations form a closed…
In this paper we provide an analytical procedure which leads to a system of $(n-2)^2$ polynomial equations whose solutions give the parameterisation of the complex $n\times n$ Hadamard matrices. It is shown that in general the Hadamard…
Hermitian mass matrices for the up and down quarks with texture zeroes but with the minimum number of parameters, ten, are investigated. We show how these {\em minimum parameter} forms can be obtained from a general set of hermitian…
Non-Hermitian Hamiltonians H possess the real (i.e., observable) spectra inside certain specific domains of parameters D. In general, the determination of their observability-horizon boundaries is difficult. We list the pseudo-Hermitian…
The task of analytically diagonalizing a tridiagonal matrix can be considerably simplified when a part of the matrix is uniform. Such quasi-uniform matrices occur in several physical contexts, both classical and quantum, where…
We give a minimal list of inequalities characterizing the possible eigenvalues of a set of Hermitian matrices with positive semidefinite sum of bounded rank. This answers a question of A. Barvinok.
We characterize the relationship between the singular values of a complex Hermitian (resp., real symmetric, complex symmetric) matrix and the singular values of its off-diagonal block. We also characterize the eigenvalues of an Hermitian…
We consider dynamically defined Hermitian matrices generated from orbits of the doubling map. We prove that their spectra fall into the GUE universality class from random matrix theory.
We consider a two-parameter non hermitean quantum-mechanical hamiltonian that is invariant under the combined effects of parity and time reversal transformation. Numerical investigation shows that for some values of the potential parameters…
For any real diagonalizable matrix with complex eigenvalues we provide a real, coordinate free decomposition with a clear geometric interpretation.
The eigenvalue problem of the spherically symmetric oscillator Hamiltonian is revisited in the context of canonical raising and lowering operators. The Hamiltonian is then factorized in terms of two not mutually adjoint factorizing…
We consider random matrix ensembles on the set of Hermitian matrices that are heavy tailed, in particular not all moments exist, and that are invariant under the conjugate action of the unitary group. The latter property entails that the…
In a previous paper, one of us pointed out that the anomalous dimension matrices for all physical processes that have been calculated to date are complex symmetric, if stated in an orthonormal basis. In this paper we prove this fact and…
As an application of the representation theory for the dihedral groups, we study the symmetric central configurations in the n-body problem where $n$ equal masses are placed at the vertices of a regular $n$-gon. Since the Hessian matrices…
The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…