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Non-linear Fourier analysis on compact groups is used to construct an orthonormal basis of the physical (gauge invariant) Hilbert space of Hamiltonian lattice gauge theories. In particular, the matrix elements of the Hamiltonian operator…
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…
The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization.…
The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor in interacting chaotic few- and many-body systems,…
An algebraic method for evaluating bare nucleon matrix elements of quark operators is proposed. Thereby, bare nucleon matrix elements are traced back to vacuum matrix elements. The method is similar to the soft pion theorem. Matrix elements…
We have developed a McMurchie-Davidson-like recursion formula for efficient evaluation of the Coulomb attraction and interaction matrix elements between two-dimensional primitive Cartesian Gaussian type orbitals. We also present recurrence…
Spatially-structured laser beams, eventually carrying orbital angular momentum, affect electronic transitions of atoms and their motional states in a complex way. We present a general framework, based on the spherical tensor decomposition…
Precision tests of the Standard Model and searches for beyond the Standard Model physics often require nuclear structure input. There has been a tremendous progress in the development of nuclear ab initio techniques capable of providing…
We give a formula to calculate a matrix element of a conserved current in the effective quantum mechanics defined by the wave function equivalent potentials proposed by HAL QCD collaboration. As a first step, a non-relativistic field theory…
Employing a relativistic version of a hypervirial result, recurrence relations for arbitrary non-diagonal radial hydrogenic matrix elements have recently been obtained in Dirac relativistic quantum mechanics. In this contribution honoring…
We discuss the fluctuation properties of diagonal matrix elements in the semiclassical limit in chaotic systems. For extended observables, covering a phase space area of many times Planck's constant, both classical and quantal distributions…
Covariance matrices are a useful tool to investigate correlations and entanglement in quantum systems. They are widely used in continuous variable systems, but recently also for finite dimensional systems powerful entanglement criteria in…
Using a relation between a bi-orthogonal set of equiseparable bases and the weak values of the density matrix we derive an explicit formula for its tomographic reconstruction completely analogous to the standard mutually unbiased bases…
We present a quantum theory for the dynamic structure factors in non-equilibrium, correlated, two-component systems such as plasmas or warm dense matter. Using this general framework, we derive expressions for effective local field…
We extend the former matrix rearrangement approach of the entangling power to the general cases, without the requirement of the same dimensions of the subsystems. The entangling power of a unitary operator is completely determined by its…
The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem.…
For many classically chaotic systems it is believed that the quantum wave functions become uniformly distributed, that is the matrix elements of smooth observables tend to the phase space average of the observable. In this paper we study…
The calculation of off-diagonal matrix elements has various applications in fields such as nuclear physics and quantum chemistry. In this paper, we present a noisy intermediate scale quantum algorithm for estimating the diagonal and…
A novel approach to electronic correlations in magnetic crystals which takes into account a dynamical many-body effects is present. In order to to find a frequency dependence of the electron self energy, an effective quantum-impurity…
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…