Related papers: Solving Single and Many-body Quantum Problems: A N…
Due to its great importance for applications, we generalize and extend the approach of our previous papers to study aspects of the quantum and classical dynamics of a $4$-body system with equal masses in {\it $d$}-dimensional space with…
A simple method has been introduced to furnish the equilibrium solution of the Wigner equation for all order of the quantum correction. This process builds up a recursion relation involving the coefficients of the different power of the…
It has been argued that despite remarkable success, existing random matrix theories are not adequate to describe disordered conductors in the metallic regime, due to the presence of certain two-body interactions in the effective Hamiltonian…
We construct a family of quasi-solvable quantum many-body systems by an algebraic method. The models contain up to two-body interactions and have permutation symmetry. We classify these models under the consideration of invariance property.…
In this paper a novel numerical approximation of parametric eigenvalue problems is presented. We motivate our study with the analysis of a POD reduced order model for a simple one dimensional example. In particular, we introduce a new…
This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a…
Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…
A method based on the envelope theory is presented to compute approximate solutions for $N$-body Hamiltonians with identical particles in $D$ dimensions ($D\ge 2$). In some favorable cases, the approximate eigenvalues can be analytically…
We explicate a procedure to solve general linear differential equations, which connects the desired solutions to monomials x^m of an appropriate degree m. In the process the underlying symmetry of the equations under study, as well as that…
The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer…
We give a brief overview of a simple and unified way, called the prepotential approach, to treat both exact and quasi-exact solvabilities of the one-dimensional Schr\"odinger equation. It is based on the prepotential together with Bethe…
Quantum embedding theories are powerful tools for approximately solving large-scale strongly correlated quantum many-body problems. The main idea of quantum embedding is to glue together a highly accurate quantum theory at the local scale…
We propose a numerical homogenization method for scalar linear partial differential equations with rough coefficients, that integrates classical coarse-scale solvers with quantum subroutines for fine-scale corrections. Inspired by the…
Different hybrid quantum-classical algorithms have recently been developed as a near-term way to solve linear systems of equations on quantum devices. However, the focus has so far been mostly on the methods, rather than the problems that…
This work investigates a new approach to find closed form analytical approximate solution of linear initial value problems. Classical Bernoulli polynomials have been used to derive a finite set of orthonormal polynomials and a finite…
Background: The numerical solution of few-body scattering problems with realistic interactions is a difficult problem that normally must be solved on powerful supercomputers, taking a lot of computer time. This strongly limits the…
Knowledge of all correlation functions of a system is equivalent to solving the corresponding many-body problem. Already a finite set of correlation functions can be sufficient to describe a quantum many-body system if correlations…
Quantum many-body theory has witnessed tremendous progress in various fields, ranging from atomic and solid-state physics to quantum chemistry and nuclear structure. Due to the inherent computational burden linked to the ab initio treatment…
The classical simulation of quantum systems typically requires exponential resources. Recently, the introduction of a machine learning-based wavefunction ansatz has led to the ability to solve the quantum many-body problem in regimes that…
We have suggested a method for treating different quantum few-body dynamics without usual partial-wave analysis. With this approach new results were obtained in the physics of ultracold atom-atom collisions and ionization and…