相关论文: Projector operators for the no-core shell model
We demonstrate the existence of multiple converging sequences in the ab initio no-core shell model. By examining the underlying theory of effective operators, we expose the physical foundations for the alternative pathways to convergence.…
In a recent paper the notion of {\em quantum perceptron} has been introduced in connection with projection operators. Here we extend this idea, using these kind of operators to produce a {\em clustering machine}, i.e. a framework which…
No-core shell model (NCSM) calculations using ab initio effective interactions are very successful in reproducing experimental nuclear spectra. The main theoretical approach is the use of effective operators, which include correlations left…
Projection-based integrators are effectively employed in high-precision systems with growing industrial success. By utilizing a projection operator, the resulting projection-based integrator keeps its input-output pair within a designated…
Projection operators are important in Analysis, Optimization and Algorithm. It is well known that these operators are firmly nonexpansive. In this paper, we provide an exact result that sharpens this well-known result. We develop the theory…
The problem of construction of projection operators on eigen-subspaces of symmetry operators is considered. This problem arises in many approximate methods for solving time-independent and time-dependent quantum problems, and its solution…
The purpose of this article is to study operators whose kernel share some key features of Bergman kernels from complex analysis, and are approximate projectors. It turns out that they must be associated with a rich set of geometric data, on…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
Several algebraic and topological properties of subgradient projection operators are investigated and various examples are provided. Connections with Moreau's proximity operator are also made and acceleration schemes for subgradient…
In this work we consider an iterative method for solving the quasi-convex feasibility problem. We firstly introduce the so-called star subgradient projection operator and present some useful properties. We subsequently obtain a convergence…
An overview of the ab initio no-core shell model is presented. Recent results for light nuclei obtained with the chiral two-nucleon and three-nucleon interactions are highlighted. Cross section calculations of capture reactions important…
The Koopman operator framework provides a perspective that non-linear dynamics can be described through the lens of linear operators acting on function spaces. As the framework naturally yields linear embedding models, there have been…
We describe the representation of arbitrary density operators in terms of expectation values of simple projection operators. Two representations are presented which yield non--recursive schemes for experimentally determining the density…
A projection operator technique for solution of relativistic wave equation on non-compact group has been proposed. This technique was applied to the construction of wave equations for charged vector boson in a potential field. The equations…
Working in the framework of the ab-initio no-core shell model, we derive two-body effective interactions microscopically for specific harmonic-oscillator basis spaces from the realistic Argonne V8' nucleon-nucleon potential. However, our…
In this paper we study the Weihrauch complexity of projection operators onto closed subsets of the Euclidean space. We show that some fundamental degrees of the Weihrauch lattice can be characterized in terms of such operators.
Following the construction of the projection operators on $T^2$ presented by Gopakumar, Headrick and Spradlin, we construct a set of projection operators on the integral noncommutative orbifold $T^2/G (G=Z_N, N=2, 3, 4, 6)$ which correspond…
We characterize the semiclosed projections and apply them to compute the Schur complement of a selfadjoint operator with respect to a closed subspace. These projections occur naturally when dealing with weak complementability.
This article introduces two new fractional operators with sine ($\sin$) and cosine ($\cos$) kernels, motivated by their fundamental role in modeling AC signals in electrical circuits. The operators are designed to improve the analysis of…
We report on recent microscopic calculations of reaction properties based upon the nuclear structure of the ab initio no-core shell model (NCSM).