Theoretical condensed matter physics aims at constructing
``simple'' models that can describe the phenomenology observed
in crystalline solids, amorphous materials, rubber like materials, fluids, etc.
Some of the great triumphs of condensed matter theory have been to
provide a simple and coherent picture for such diverse phenomena as
the existence of crystalline, magnetic, metallic, and superconducting
states of matter. More mundane (though highly non-trivial) questions
such as how does paper crumble have also been addressed with the tools
of theoretical condensed matter physics. At the multidisciplinary
frontiers of theoretical condensed matter physics, models for earthquakes,
protein folding, HIV, stock-market, automobile traffic, etc,
have been proposed. Traditionally, all these systems have been thought of,
to some extent, as very large collections of ``simple'' identical
constituents that interact according to some set of rules.
(With the emergence of nanotechnology, it is now possible to study
very small collections of simple constituents in contact with
``large reservoirs''. This is the field of mesoscopic physics.)
For example, if one is interested in the vibrational modes of a crystal,
the ``simple'' constituent is an atom and, to a first approximation,
the interaction between two neighboring atoms is a linear restoring force.
In another example, if one is interested in the effect of shaking
a sand-glass one can start with the simplification
that each sand-grain is a sphere
and that no two sand-grain can overlap in the sand-glass.
The essential difference between these two examples arises
from the relevant length and time scales.
Because of its tiny size a single atom obeys the rules of quantum mechanics
whereas the much larger sand grain obeys the rules of classical mechanics.
Keeping in mind this important difference,
the challenge to the condensed matter physicist is, in both cases,
to extract what properties of these complex
(by the very large number of the elementary constituents)
systems can be measured and calculated reliably.
In turn a sufficiently detailed knowledge
of intrinsic properties of complex system
can serve as a definition of a more general phenomenon that might even
transcend the given complex system.
For example, the existence of vibrational modes in a crystal is the
manifestation of the phenomenon of spontaneous symmetry breaking,
a phenomenon that applies more generally to magnets, superconductors,
the electro-weak interaction, etc.
Another example is that of a conventional metal as defined by the property
that the resistivity obeys a certain power law dependence on temperature
at sufficiently low temperatures. This property can be entirely ascribed
to the fact that a gas of electron is responsible for charge transport
in a metal and that quantum mechanics tells us that electrons
obey the so-called Fermi-Dirac statistics. This is why microscopically
different materials, say Li, Na, K, Rb, Cs, Cu, Ag, etc,
share the same temperature dependence of their resistivity at
low temperatures, i.e., are all metals at a macroscopic scale.
Dr. Christopher Mudry
Paul Scherrer Institut
WHGA/125
CH-5232 Villigen PSI
Switzerland