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Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
By using the plane-wave expansion for the electromagnetic-field vector potential, transition matrix elements between the relativistic bound and unbound states of hydrogenic atoms were expressed explicitly in terms of finite series made of…
Matrix element reweighting is a powerful experimental technique widely employed to maximize the amount of information that can be extracted from a collider data set. We present a procedure that allows to automatically evaluate the weights…
Many quantum statistical models are most conveniently formulated in terms of non-orthonormal bases. This is the case, for example, when mixtures and superpositions of coherent states are involved. In these instances, we show that the…
Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…
The functional Schrodinger picture formulation of quantum field theory and the variational Gaussian approximation method based on the formulation are briefly reviewed. After presenting recent attempts to improve the variational…
With a view to applying the Generator Coordinate Method to large configuration spaces, we propose a simple approximate formula to compute diabatic many-body matrix elements without having to evaluate two-body interaction matrix elements.…
Matrix elements between nonorthogonal Slater determinants represent an essential component of many emerging electronic structure methods. However, evaluating nonorthogonal matrix elements is conceptually and computationally harder then…
Theory of the quantum quartic oscillator is developed with close attention to the energy cutoff one needs to impose on the system in order to approximate the smallest eigenvalues and corresponding eigenstates of its Hamiltonian by…
We present some new mathematical tools which help to derive information about the quark mass matrices directly from experimental data and to elucidate the structure of these mass matrices.
The techniques for polynomial interpolation and Gaussian quadrature are generalized to matrix-valued functions. It is shown how the zeros and rootvectors of matrix orthonormal polynomials can be used to get a quadrature formula with the…
The operator and the functional formulations of the dynamics of constrained systems are explored for determining unambiguously the quantum Hamiltonian of a nonrelativistic particle in a curved space.
Within the framework of the quark model and the variational method, the bound states of four heavy quarks (tetraquarks) are investigated. The basis variational wave functions are chosen in the Gaussian form. The matrix elements of the…
Analytic perturbation theory for matrices and operators is an immensely useful mathematical technique. Most elementary introductions to this method have their background in the physics literature, and quantum mechanics in particular. In…
A conversion matrix approach to solving network problems involving time-varying circuit components is applied to the method of moments for electromagnetic scattering analysis. Detailed formulations of this technique's application to the…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…
I report on the application of tmQCD techniques to the computation of hadronic matrix elements of four-fermion operators. Emphasis is put on the computation of $B_K$ in quenched QCD performed by the ALPHA Collaboration. The extension of…
A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects. Considerable improvement results from separation of…
Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in problems of mathematics, statistics and natural sciences. In this article we start considering the case of a Gauss hypergeometric…
A review of methods for finding general expressions for matrix elements (non-diagonal with respect to configurations included) of any one- and two-particle operator for an arbitrary number of shells in an atomic configuration is given.…