相关论文: Instruction of my personal computing library
The Spinsim python package simulates spin-half and spin-one quantum mechanical systems following a time dependent Shroedinger equation. It makes use of numba.cuda, which is an LLVM (Low Level Virtual Machine) compiler for Nvidia Cuda…
We present a new open source C library \texttt{msolve} dedicated to solving multivariate polynomial systems of dimension zero through computer algebra methods. The core algorithmic framework of \texttt{msolve} relies on Gr\''obner bases and…
The rich phenomenology of quantum many-body systems such as atomic nuclei is complex to interpret. Often, the behaviour (e.g. evolution with the number of constituents) of measurable/observable quantities such as binding or excitation…
Certain complex-contour (a.k.a. quantum-toboggan) generalizations of Schroedinger's bound-state problem are reviewed and studied in detail. Our key message is that the practical numerical solution of these atypical eigenvalue problems may…
This paper introduces torchsom, an open-source Python library that provides a reference implementation of the Self-Organizing Map (SOM) in PyTorch. This package offers three main features: (i) dimensionality reduction, (ii) clustering, and…
We outline a remarkably efficient method for generating solutions to quantum anharmonic oscillators with an x^{2M} potential. We solve the Schroedinger equation in terms of a free parameter which is then tuned to give the correct boundary…
This paper presents tensorflow-riemopt, a Python library for geometric machine learning in TensorFlow. The library provides efficient implementations of neural network layers with manifold-constrained parameters, geometric operations on…
Using the Wentzel-Kramers-Brillouin method, we derive a modified form of the Thomas-Fermi approximation to electron density. This new result enables us to calculate the details of the self-consistent ion cores, as well as the ionization…
We present the library Collier for the numerical evaluation of one-loop scalar and tensor integrals in perturbative relativistic quantum field theories. The code provides numerical results for arbitrary tensor and scalar integrals for…
We describe version 2 of the SPICE dataset, a collection of quantum chemistry calculations for training machine learning potentials. It expands on the original dataset by adding much more sampling of chemical space and more data on…
In this paper we review the calculations that are needed to obtain the bosonic and fermionic effective potential at finite temperature and volume (at one loop). The calculations at finite volume correspond to $S^1\times R^d$ topology. These…
Recent advances in machine learning have facilitated numerically accurate solution of the electronic Schr\"{o}dinger equation (SE) by integrating various neural network (NN)-based wavefunction ansatzes with variational Monte Carlo methods.…
Schr\"odinger equations with nonlinearities concentrated in some regions of space are good models of various physical situations and have interesting mathematical properties. We show that in the semiclassical limit it is possible to…
Loop quantum cosmology is a symmetry-reduced application of loop quantum gravity that has led to the resolution of classical singularities such as the big bang, and those at the center of black holes. This can be seen through numerical…
This work presents a direct and highly accurate method to solve ordinary differential equations, in particular the Schr\"odinger equation in one dimension, through the direct substitution of a power series solution to obtain a purely…
We study {{\rm C}$_{60}$} with the use of Thomas-Fermi theory. A spherical shell model is invoked to treat the nuclear potential, where the nuclear and core charges are smeared out into a shell of constant surface charge density. The…
This paper introduces students and instructors to the use of Scilab for calculating phase shifts from phenomenological potentials in nuclear, atomic, and molecular scattering, beginning with a Riccati-type nonlinear differential equation…
We discussed exact solutions of the Schroedinger equation for a two-dimensional parabolic confinement potential in a homogeneous external magnetic field. It turns out that the two-electron system is exactly solvable in the sense, that the…
We study the complexity of approximating the smallest eigenvalue of a univariate Sturm-Liouville problem on a quantum computer. This general problem includes the special case of solving a one-dimensional Schroedinger equation with a given…
Self-gravity plays an important role in the evolution of rotationally supported systems such as protoplanetary disks, accretion disks around black holes, or galactic disks, as it can both feed turbulence or lead to gravitational…