Related papers: Computer Algebra in Particle Physics
It is shown that for a large class of non-holonomic quantum mechanical systems one can make the computation of BRST charge fully algorithmic. Two computer algebra programs written in the language of {\tt REDUCE} are described. They are able…
We show how the computer algebra system OSCAR can be used to obtain topologically correct or visually pleasing drawings of real plane algebraic curves.
We investigate the computational power of particle methods, a well-established class of algorit hms with applications in scientific computing and computer simulation. The computational power of a compute model determines the class of…
Much of the research done by modern physicists would be impossible without the use of computation. And yet, while computation is a crucial tool of practicing physicists, physics curricula do not generally reflect its importance and utility.…
The advent of electronic computers has revolutionised the application of statistical mechanics to the liquid state. Computers have permitted, for example, the calculation of the phase diagram of water and ice and the folding of proteins.…
As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a…
In this paper, the application of quantum simulations and quantum machine learning to solve low-energy nuclear physics problems is explored. The use of quantum computing to deal with nuclear physics problems is, in general, in its infancy…
A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.
We survey group-theoretic algorithms for finding (some or all) subgroups of a finite group and discuss the implementation of these algorithms in the computer algebra system GAP
Intended for mathematical physicists interested in applications of the division algebras to physics, this article highlights some of their more elegant properties with connections to the theories of Galois fields and quadratic residues.
Most relatively modern desktop or even laptop computers contain a graphics card useful for more than showing colors on a screen. In this paper, we make a case for why you should learn enough about GPU (graphics processing unit) computing to…
In the recent years, Hopf algebras have been introduced to describe certain combinatorial properties of quantum field theories. I will give a basic introduction to these algebras and review some occurrences in particle physics.
We review Grover's algorithm by means of a detailed geometrical interpretation and a worked out example. Some basic concepts of Quantum Mechanics and quantum circuits are also reviewed. This work is intended for non-specialists which have…
Particle suspensions are ubiquitous in our daily life, but are not well understood due to their complexity. During the last twenty years, various simulation methods have been developed in order to model these systems. Due to varying…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
Clifford algebras have broad applications in science and engineering. The use of Clifford algebras can be further promoted in these fields by availability of computational tools that automate tedious routine calculations. We offer an…
Machine learning encompasses a set of tools and algorithms which are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting…
The aim of this paper is to propose a strategy to implement the Minimal Model Program in modern computer algebra systems.
One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In…
These notes provide an introduction to standard topics on quantum computation and communication for those who already have a basic knowledge of quantum mechanics. The main target audience are professional physicists as well as advanced…