相关论文: Numerical diagonalization of fermion mass matrices
Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…
A motivation is given for expressing classical mechanics in terms of diagonal projection matrices and diagonal density matrices. Then quantum mechanics is seen to be a simple generalization in which one replaces the diagonal real matrices…
Understanding the structure of the fermion mixing matrices is an important question in particle physics. The quark mixing matrix is approximately diagonal while the lepton mixing matrix has large off-diagonal elements. Attempting to…
This paper proposes a Newton-type method to solve numerically the eigenproblem of several diagonalizable matrices, which pairwise commute. A classical result states that these matrices are simultaneously diagonalizable. From a suitable…
A simple extension of the standard model is proposed in which all the three generations of neutrinos are Dirac particles and are naturally light. We then assume that the neutrino mass matrix is diagonal and degenerate, with a few eV mass to…
This paper is concerned with computations of a few smaller eigenvalues (in absolute value) of a large extremely ill-conditioned matrix. It is shown that smaller eigenvalues can be accurately computed for a diagonally dominant matrix or a…
The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…
This paper studies the problem of reconstructing binary matrices that are only accessible through few evaluations of their discrete X-rays. Such question is prominently motivated by the demand in material science for developing a tool for…
In a series of recent papers we have shown how the dynamical behavior of certain classical systems can be analyzed using operators evolving according to Heisenberg-like equations of motions. In particular, we have shown that raising and…
The large freedom in the SM fermionic mass matrices allows for large LH and LH quark rotations. This is a natural possibility in view of the observed large leptonic mixing. Proton decay and especially its gauge mediated decay is sensitive…
It is well known that a set of non-defect matrices can be simultaneously diagonalized if and only if the matrices commute. In the case of non-commuting matrices, the best that can be achieved is simultaneous block diagonalization. Here we…
The mass matrices of charged fermions have a simple structure if expressed in powers of the small parameter sigma=(m_c/m_t)^{1/2}. It is suggested that the mass matrix of the three heavy neutrinos occuring in grand unified theories can be…
We study a variety of different texture patterns in the basis in which the charged lepton mass matrix or neutrino mass matrix or neither are diagonal. The experimental results on the neutrinos provide sufficient restrictions to allow only a…
Within the framework of quark mass matrices with a democratic texture, the unitary rotation matrices that diagonalize the quark matrices are obtained by a specific parametrization of the Cabibbo-Kobayashi-Maskawa mixing matrix. Different…
Status of determination of the neutrino masses and mixing is formulated and possible uncertainties, especially due to presence of the sterile neutrinos, are discussed. The data hint an existence of special ``neutrino'' symmetries. If not…
The inversion of gravitational lens systems is hindered by the fact that multiple mass distributions are often equally compatible with the observed properties of the images. Besides using clear examples to illustrate the effect of the…
We show how to visualize the process of diagonalizing the Hamiltonian matrix to find the energy eigenvalues and eigenvectors of a generic one-dimensional quantum system. Starting in the familiar sine-wave basis of an embedding infinite…
This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…
We investigate numerically efficient approximations of eigenspaces associated to symmetric and general matrices. The eigenspaces are factored into a fixed number of fundamental components that can be efficiently manipulated (we consider…
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…