24 - Low temperatures and degenerate systems

Summary

In this chapter we return to the study of systems that are nearly degenerate. As illustrated in Figure 24.1, a degenerate system of N identical fermions fills the N lowest quantum states, one particle per state. For degenerate bosons, all are in the one single state of lowest energy.

A degenerate system is confined to a small volume in phase space because of either:

• restricted volume in momentum space owing to small masses, or low temperatures, or

• Restricted volume in coordinate space owing to high densities.

Important examples of each case will be studied in this chapter.

The measures of high densities, small masses, and low temperatures are on a relative scale and are interdependent. At earthly densities, many systems become degenerate only if temperatures descend to a few kelvins or lower. Yet these same systems may be degenerate at several million kelvins when squashed together in extremely dense collapsed stars. The conduction electrons in metals have the same density and temperature as the atoms. Yet because of the difference in their masses, the electrons are degenerate and the atoms are not.

At high temperatures and/or low densities, the particles of a system are surrounded by vacant quantum states into which they can move (Figure 24.1). This freedom enables them to give rather smooth and continuous responses to varying environmental conditions. But in degenerate systems, quantum effects are more visible. Imprisoned particles are unable to move into neighboring states, which makes the system unresponsive to external stimuli.