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.
