Degenerate Matter - Concept

Concept

Imagine that a plasma is cooled and compressed repeatedly. Eventually, it will not be possible to compress the plasma any further, because the exclusion principle states that two fermions cannot share the same quantum state. When in this state, since there is no extra space for any particles, we can also say that a particle's location is extremely defined. Therefore, since (according to the Heisenberg uncertainty principle) ΔpΔx ≥ ħ/2 where Δp is the uncertainty in the particle's momentum and Δx is the uncertainty in position, then we must say that their momentum is extremely uncertain since the particles are located in a very confined space. Therefore, even though the plasma is cold, the particles must be moving very fast on average. This leads to the conclusion that if you want to compress an object into a very small space, you must use tremendous force to control its particles' momentum.

Unlike a classical ideal gas, whose pressure is proportional to its temperature (P=nkT/V, where P is pressure, V is the volume, n is the number of particles—typically atoms or molecules—k is Boltzmann's constant, and T is temperature), the pressure exerted by degenerate matter depends only weakly on its temperature. In particular, the pressure remains nonzero even at absolute zero temperature. At relatively low densities, the pressure of a fully degenerate gas is given by P=K(n/V)5/3
, where K depends on the properties of the particles making up the gas. At very high densities, where most of the particles are forced into quantum states with relativistic energies, the pressure is given by P=K'(n/V)4/3
, where K' again depends on the properties of the particles making up the gas.

All matter experiences both normal thermal pressure and degeneracy pressure, but in commonly encountered gases, thermal pressure dominates so much that degeneracy pressure can be ignored. Likewise, degenerate matter still has normal thermal pressure, but at extremely high densities the degeneracy pressure usually dominates.

Exotic examples of degenerate matter include neutronium, strange matter, metallic hydrogen and white dwarf matter. Degeneracy pressure contributes to the pressure of conventional solids, but these are not usually considered to be degenerate matter because a significant contribution to their pressure is provided by electrical repulsion of atomic nuclei and the screening of nuclei from each other by electrons. In metals it is useful to treat the conduction electrons alone as a degenerate, free electron gas while the majority of the electrons are regarded as occupying bound quantum states. This contrasts with degenerate matter that forms the body of a white dwarf, where all the electrons would be treated as occupying free particle momentum states.