Related papers: Lowest eigenvalue of the nuclear shell model Hamil…
A practical computation method to find the eigenvalues and eigenspinors of quantum mechanical Hamiltonian is presented. The method is based on reduction of the eigenvalue equation to well known geometric algebra rotor equation and,…
We develop a computational method to learn a molecular Hamiltonian matrix from matrix-valued time series of the electron density. As we demonstrate for three small molecules, the resulting Hamiltonians can be used for electron density…
We study the eigenvalue trajectories of a time dependent matrix $ G_t = H+i t vv^*$ for $t \geq 0$, where $H$ is an $N \times N$ Hermitian random matrix and $v$ is a unit vector. In particular, we establish that with high probability, an…
We give a complete geometrical description of the effective Hamiltonians common in nuclear shell model calculations. By recasting the theory in a manifestly geometric form, we reinterpret and clarify several points. Some of these results…
It is studied that `no-scale' model makes hierarchy between scalar top mass and Z boson mass naturally. The supersymmetry breaking parameters are constrained by flavor changing neutral currents in minimal supersymmetric standard model. One…
This work presents the first calculation of the lowest moment of the forward Compton structure function $\mathcal{F}_2$ for a multi-nucleon deuteron-like state using Feynman-Hellmann lattice QCD techniques. Using this result as a…
This paper considers a nuclear norm penalized estimator for panel data models with interactive effects. The low-rank interactive effects can be an approximate model and the rank of the best approximation unknown and grow with sample size.…
We propose a convex variational principle to find sparse representation of low-lying eigenspace of symmetric matrices. In the context of electronic structure calculation, this corresponds to a sparse density matrix minimization algorithm…
A common challenge faced in quantum physics is finding the extremal eigenvalues and eigenvectors of a Hamiltonian matrix in a vector space so large that linear algebra operations on general vectors are not possible. There are numerous…
The nuclear matrix elements that govern the rate of neutrinoless double beta decay must be accurately calculated if experiments are to reach their full potential. Theorists have been working on the problem for a long time but have recently…
Hierarchical matrices (usually abbreviated ${\mathcal H}$-matrices) are frequently used to construct preconditioners for systems of linear equations. Since it is possible to compute approximate inverses or $LU$ factorizations in ${\mathcal…
We propose a quantum algorithm for inferring the molecular nuclear spin Hamiltonian from time-resolved measurements of spin-spin correlators, which can be obtained via nuclear magnetic resonance (NMR). We focus on learning the anisotropic…
This paper establishes a new comparison principle for the minimum eigenvalue of a sum of independent random positive-semidefinite matrices. The principle states that the minimum eigenvalue of the matrix sum is controlled by the minimum…
A model subspace configuration interaction method is developed to obtain chemically accurate electron correlations by diagonalising a very compact effective Hamiltonian of realistic molecule. The construction of the effective Hamiltonian is…
We present and analyze an efficient implementation of an iteratively reweighted least squares algorithm for recovering a matrix from a small number of linear measurements. The algorithm is designed for the simultaneous promotion of both a…
The nonzero eigenvalues of $AB$ are equal to those of $BA$: an identity that holds as long as the products are square, even when $A,B$ are rectangular. This fact naturally suggests an efficient algorithm for computing eigenvalues and…
A fundamental problem in the theory of PT-invariant quantum systems is to determine whether a given system `respects' this symmetry or not. If not, the system usually develops non-real eigenvalues. It is shown in this contribution how to…
The impact of applying state-of-the-art tensor factorization techniques to modern nuclear Hamiltonians derived from chiral effective field theory is investigated. Subsequently, the error induced by the tensor decomposition of the input…
The prediction of possible ordering of neutrino masses relies mostly on the model selected. Alienating the $\mu-\tau$ interchange symmetry from discrete flavour symmetry based models, turns the neutrino mass matrix less predictive. But this…
Key properties of physical systems can be described by the eigenvalues of matrices that represent the system. Computational algorithms that determine the eigenvalues of these matrices exist, but they generally suffer from a loss of…