Related papers: On generation of the Bargmann-Moshinsky basis of S…
A FORTRAN code for generating the leading SU(3) irreducible representation (irrep) of N identical spin 1/2 fermions in a harmonic oscillator mean field is introduced. The basis states are labeled by N--the total number of particles, the…
We find an algorithm of numerical renormalization group for spin chain models. The essence of this algorithm is orthogonal transformation of basis states, which is useful for reducing the number of relevant basis states to create effective…
Boltzmann Machines (BMs) are graphical models with interconnected binary units, employed for the unsupervised modeling of data distributions. When trained on real data, BMs show the tendency to behave like critical systems, displaying a…
An obstacle encountered in applying orthogonal-polynomials fitting is how to select out the proper fitting expression. By adding a Laplace term to the error expression and introducing the concept of overfitting degree, a regularization and…
We consider several variants of SU(3) partial dynamical symmetry in relation to quadrupole shapes in nuclei. Explicit construction of Hamiltonians with such property is presented in the framework of the interacting boson model (IBM),…
While an explicit basis is common in the study of Euclidean spaces, it is usually implied in the study of inertial relativistic systems. There are some conceptual advantages to including the basis in the study of special relativistic…
We show that the Q-box expansion of nuclear many-body physics can be applied in nuclear effective field theory with explicit pions and external sources. We establish the corresponding power counting and give an algorithm for the…
We present a computer code that analytically evaluates the matrix elements of the microscopic nuclear Hamiltonian and unity operator between Slater determinants of displaced gaussian single particle orbits. Such matrix elements appear in…
In numerical simulations of many charged systems at the micro/nano scale, a common theme is the repeated solution of the Poisson-Boltzmann equation. This task proves challenging, if not entirely infeasible, largely due to the nonlinearity…
We construct a basis for a modified quantum group of finite type, extending the PBW bases of positive and negative halves of a quantum group. Generalizing Lusztig's classic results on PBW bases, we show that this basis is orthogonal with…
The most common method for calculating accurate numerical solutions for complicated linear differential equations - for example, finding eigenvalues and eigenfunctions of the Schrodinger equation for many-electron atoms - is the variational…
The norm kernel of the generator-coordinate method is shown to be a symmetric kernel of an integral equation with eigenfunctions defined in the Fock--Bargmann space and forming a complete set of orthonormalized states (classified with the…
The description of weakly bound electronic states is especially difficult with atomic orbital basis sets. The diffuse atomic basis functions that are necessary to describe the extended electronic state generate significant linear…
We propose to use the modified Gram -- Schmidt orthonormalization process in Minkowski space for construction of orthonormal bases from the vectors of the problem.
We analyze a variety of integration schemes for the momentum space functional renormalization group calculation with the goal of finding an optimized scheme. Using the square lattice $t-t'$ Hubbard model as a testbed we define and benchmark…
The problem of construction of Barabanov norms for analysis of properties of the joint (generalized) spectral radius of matrix sets has been discussed in a number of publications. In previous papers of the author the method of Barabanov…
We carry further our work [DV2] on orthonormal integrators based on Householder and Givens transformations. We propose new algorithms and pay particular attention to appropriate implementation of these techniques. We also present a suite of…
We present a new approach for the Talmi-Moshinsky transformation representation in the harmonic oscillator basis. We utilize the SU(3) scheme for the calculation of harmonic oscillator brackets. Using this scheme we obtain the explicit…
A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space…
We review the role played by long-distance symmetries within the context of the similarity renormalization group approach. This is based on phase-shift-preserving continuous unitary transformations that evolve Hamiltonians with a cutoff on…