Related papers: COMBINATORIAL COMPUTATION OF CLEBSCH-GORDAN COEFFI…
We present a numerical scheme for efficiently extracting the higher-order moments and cumulants of various operators on spin systems represented as tensor product states, for both finite and infinite systems, and present several…
The sectional curvature of a compact Riemannian manifold M can be seen as a random variable on the Grassmann bundle of 2-planes in TM endowed with the Fubini-Study volume density. In this article we calculate the moments of this random…
Contraction coefficients give a quantitative strengthening of the data processing inequality. As such, they have many natural applications whenever closer analysis of information processing is required. However, it is often challenging to…
A generalization of classical cubic B-spline functions with a parameter is used as basis in the collocation method. Some initial boundary value problems constructed on the nonlinear Klein-gordon equation are solved by the proposed method…
Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…
The paper contains the derivation of a general set of recurrence formulas for the calculus of the SU(3) Clebsch-Gordan coefficients. The first six sections are introductory, presenting the notations and placing SU(3) in the framework of the…
Calculating the spectral function of two dimensional systems is arguably one of the most pressing challenges in modern computational condensed matter physics. While efficient techniques are available in lower dimensions, two dimensional…
The leading order evolution of parton orbital angular momenta is treated in the probabilistic manner. As a result, the splitting probability matrix, while coinciding with the recent explicit calculations, is expressed in the terms of the…
Using purely combinatorial methods we calculate the first degree cohomology of Specht modules indexed by two part partitions over fields of characteristic $p\ge 3$. These combinatorial methods also allow us to obtain an explicit description…
In this paper, two new stochastic algorithms for calculating parametric derivatives of the solution to the Smoluchowski coagulation equation are presented. It is assumed that the coagulation kernel is dependent on these parameters. The new…
We present an alternative formalism for modeling spin. The ontological elements of this formalism are base-2 sequences of length $n$. The machinery necessary to model physics is then developed by considering correlations between base-2…
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.…
This article is the second of a series of three presenting an alternative method to compute the one-loop scalar integrals. It extends the results of the first article to general complex masses. Let us remind the main features enjoyed by…
This survey provides a unified discussion of multiple integrals, moments, cumulants and diagram formulae associated with functionals of completely random measures. Our approach is combinatorial, as it is based on the algebraic formalism of…
Using condition of relativistic invariance, group theory and Clifford algebra the component Lorentz invariance generalized Dirac equation for a particle with arbitrary mass and spin is suggested, where In the case of half-integral spin…
The relativistic method of moments is one of the most successful approaches to extract second order viscous hydrodynamics from a kinetic underlying background. The equations can be systematically improved to higher order, and they have…
Coherence vectors and correlation matrices are important functions frequently used in physics. The numerical calculation of these functions directly from their definitions, which involves Kronecker products and matrix multiplications, may…
We consider secular perturbations of nearly Keplerian two-body motion under a perturbing potential that can be approximated to sufficient accuracy by expanding it to second order in the coordinates. After averaging over time to obtain the…
We define a set of orthogonal functions on the complex projective space CP^{N-1}, and compute their Clebsch-Gordan coefficients as well as a large class of 6-j symbols. We also provide all the needed formulae for the generation of…
We compute the geometric phase for a spin-1/2 particle under the presence of a composite environment, composed of an external bath (modeled by an infinite set of harmonic oscillators) and another spin-1/2 particle. We consider both cases:…