相关论文: Numerical diagonalization of fermion mass matrices

Often the easiest way to discretize an ordinary or partial differential equation is by a rectangular numerical method, in which n basis functions are sampled at m>>n collocation points. We show how eigenvalue problems can be solved in this…

We propose a new and efficient method of reconstructing quark mass matrices from their eigenvalues and a complete set of mixing observables. By a combination of the principle of NNI (nearest neighbour interaction) bases which are known to…

We consider two different types of deformations for the linear group $ GL(n)$ which correspond to using of a general diagonal R-matrix. Relations between braided and quantum deformed algebras and their coactions on a quantum plane are…

Loop corrections induce a dependence on the momentum squared of the coefficients of the Standard Model Lagrangian, making highly non-trivial (or even impossible) the diagonalization of its quadratic part. Fortunately, the introduction of…

We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…

We obtain generalisations of some inequalities for positive unital linear maps on matrix algebra. This also provides several positive semidefinite matrices and we get some old and new inequalities involving the eigenvalues of a Hermitian…

We discuss a method called quasi-sparse eigenvector diagonalization which finds the most important basis vectors of the low energy eigenstates of a quantum Hamiltonian. It can operate using any basis, either orthogonal or non-orthogonal,…

The discrete non-Abelian symmetry $A_4$, valid at some high-energy scale, naturally leads to degenerate neutrino masses, without spoiling the hierarchy of charged-lepton masses. Realistic neutrino mass splittings and mixing angles (one of…

I discuss in this talk mainly three topics related with dark matter motivated neutrino mass spectrum and a generic issue of mass pattern, the normal versus the inverted mass hierarchies. In the first part, by describing failure of a…

We give a detailed discussion of our general determination of (i) the number of unremovable, physically meaningful phases in quark mass matrices and (ii) which elements of these matrices can be rendered real by rephasings of fermion fields.…

The dynamics of fermion generations is treated in the framework of the fractional Lagrangian and Hamiltonian in the compact extra dimension. The resulting spectra for u, d, e generations are described by the only mass parameter and slightly…

Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…

It is well-known that a complex circulant matrix can be diagonalized by a discrete Fourier matrix with imaginary unit $\mathtt{i}$. The main aim of this paper is to demonstrate that a quaternion circulant matrix cannot be diagonalized by a…

The generic predictions of two-texture zero neutrino mass matrices in the flavor basis have been examined especially in relation to the degeneracies between mass matrices within a class and interesting constraints on the neutrino parameters…

In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…

The efficient inversion of matrix polynomials is a critical challenge in computational mathematics. We design a procedure to determine the inverse of matrices polynomial of multidimensional Laplace matrices. The method is based on…

Starting from a weak basis in which the up (or down) quark matrix is diagonal, we obtain an exact set of equations for the quark mass matrix elements in terms of known observables. We make a numerical analysis of the down (up) quark mass…

Branes and defects in topological Landau-Ginzburg models are described by matrix factorisations. We revisit the problem of deforming them and discuss various deformation methods as well as their relations. We have implemented these…

We introduce a new diagonalization method called quasi-sparse eigenvector diagonalization which finds the most important basis vectors of the low energy eigenstates of a quantum Hamiltonian. It can operate using any basis, either orthogonal…

Recently various phenomenological implications of the existence of extra space-time dimensions have been investigated. In this letter, we construct a model with realistic fermion mass hierarchy with (large) extra dimensions beyond the usual…