Department of Physics and Astronomy

Computational Physics: A Brief Overview

Prof. Volker E. Oberacker, Vanderbilt University

Computational physics: "physics of the third kind"

Computational physics has emerged as the new third branch of physics besides the traditional branches of experimental and theoretical physics. The purpose of computational physics is not to crunch numbers, but to gain insight. This is particularly true if scientific workstations and supercomputers are coupled to sophisticated tools of visualization. During the last decade we have witnessed an almost exponential growth in computing power. This unparalled growth has redefined the classes of physics problems we are able to solve. What seemed at the forefront of research ten years ago can now be done on a high-speed scientific workstation. Today's massively parallel supercomputers allow us to address, at a fundamental rather than phenomenological level, some of the most challenging theoretical problems of modern-day physics.

The physical world: interacting quantum many-particle systems

One basic problem that is common to many areas of physics -- and other natural sciences such as chemistry -- is the quantum many-particle problem. Theorists working in atomic, condensed matter, nuclear and astrophysics (and some areas of elementary particle physics) face a very similar challenge: how to describe, usually at the quantum level, the features of many particle systems in terms of more basic interacting constituent particles. There are essentially two different approaches to the quantum many-particle problem which might be termed phenomenological and fundamental. In the first case, one tries to simplify the physical system to such an extent that the arising physical "model" can be solved analytically or with little computational effort. This approach is often the first stage in the development of a theory. As the field begins to mature, attention shifts from simple intuitive models to a "fundamental'" understanding, i.e. one attempts to describe physical systems "ab initio" starting from the most basic equations and physical principles. Computational physicists prefer the second approach. Almost all interacting quantum many-particle systems cannot be formulated perturbatively; in fact, the interesting physical phenomenon (e.g. the ground state energy of the quantum system) is usually an infinite sum of perturbative diagrams. This means that the perturbative machinery of quantum field theory (Feynman diagrams etc.) is essentially useless, and the quantum field equations must be solved by new approximation schemes without invoking perturbation theory. Because of the complexity of quantum mechanical many-body problems this implies a numerical implementation on massively parallel architectures and requires substantial advances in both science and compuational algorithms.

Computational Physics:  Interdisciplinary Research

The essence of computational physics lies in the observation that many of the fundamental equations of physics have a similar mathematical structure: for example, the many-particle Schroedinger and Dirac equations as well as the nonrelativistic or relativistic hydrodynamics equations are all partial differential equations in space and time. All of the above-mentioned basic equations of physics can be implemented on spatial coordinate lattices; there will still be differences between many of the physics problems to be studied, for example short-range vs. long-range interactions, uniform vs. non-uniform lattice spacing etc. Nevertheless, with careful planning, computational physicists are capable of developing numerical methods and algorithms that can be utilized in a transparent manner in many subfields of physics. Computational physics is truly interdisciplinary.

Last update: July 20, 2004
 Copyright © 2004, Volker E. Oberacker
Vanderbilt University