相关论文: Numerical diagonalization of fermion mass matrices
The treatment of the quark mass plays an important role when it comes to increasing the precision of the predictions of the heavy quark expansion for inclusive heavy hadron decays. Various short-distance mass schemes have been invented to…
It turns out that a parametrization of degenerate density matrices requires a parametrization of $\mathfrak{F}=U(n)/({U(k_1)\times U(k_2)\times \cdots \times U(k_m)})\quad n=k_1 +\cdots + k_m $ where $U(k)$ denotes the set of all unitary…
Differentiable quantum dynamics require automatic differentiation of a complex-valued initial value problem, which numerically integrates a system of ordinary differential equations from a specified initial condition, as well as the…
We investigate almost-degenerate perturbation theory of eigenvalue problems, using spectral projectors, also named density matrices. When several eigenvalues are close to each other, the coefficients of the perturbative series become…
A simple iterative scheme is proposed for locating the parameter values for which a 2-parameter family of real symmetric matrices has a double eigenvalue. The convergence is proved to be quadratic. An extension of the scheme to complex…
Given a set of $p$ symmetric (real) matrices, the Orthogonal Joint Diagonalization (OJD) problem consists of finding an orthonormal basis in which the representation of each of these $p$ matrices is as close as possible to a diagonal…
Differential reformulations of field theories are often used for explicit computations. We derive a one-matrix differential formulation of two-matrix models, with the help of which it is possible to diagonalize the one- and two-matrix…
This paper deals with three technical ingredients of geometry for quantum information. Firstly, we give an algorithm to obtain diagonal basis matrices for submodules of the Z_{d}-module Z_{d}^{n} and we describe the suitable computational…
It is pointed out that the strong CP problem may have a natural solution in the context of a recently proposed dualized version of the Standard Model where Higgs fields and generations emerge naturally. Although fermions have finite…
The accurate solution of some of the main problems in numerical linear algebra (linear system solving, eigenvalue computation, singular value computation and the least squares problem) for a totally positive Bernstein-Vandermonde matrix is…
Random matrices have played an important role in many fields including machine learning, quantum information theory and optimization. One of the main research focuses is on the deviation inequalities for eigenvalues of random matrices.…
It is shown that two specific properties of the unitary matrix $V$ can be expressed directly in terms of the matrix elements and eigenvalues of the hermitian matrix $M$ which is diagonalized by $V$. These are the asymmetry $\Delta(V)=…
An important theorem in Gaussian quantum information tells us that we can diagonalise the covariance matrix of any Gaussian state via a symplectic transformation. Whilst the diagonal form is easy to find, the process for finding the…
Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while…
The triangular basis is proposed as an efficient way of analyzing general quark mass matrices. Applying the method to hermitian hierarchical matrices with five texture zeros, analytic predictions for quark mixing can be readily obtained.…
Conjugation covariants of matrices are applied to study the real algebraic variety consisting of complex Hermitian matrices with a bounded number of distinct eigenvalues. A minimal generating system of the vanishing ideal of degenerate…
We discuss a new general class of mass matrix ansatz that respects the fermion mass hierarchy and calculability of the flavor mixing matrix. This is a generalization of the various specific forms of the mass matrix that is obtained by…
In the models with vector like quark doublets, the mass matrices of up and down type quarks are related. Precise diagonalization for the mass matrices became an obstacle in the numerical studies. In this work we propose a diagonalization…
The present paper deals with the discrete inverse problem of reconstructing binary matrices from their row and column sums under additional constraints on the number and pattern of entries in specified minors. While the classical…
In a previous paper, we have given an algebraic model to the set of intervals. Here, we apply this model in a linear frame. We define a notion of diagonalization of square matrices whose coefficients are intervals. But in this case, with…