Java Statistical Distributions
This program calculates the distribution
functions for M particles in a spherical harmonic oscillator.
All three distributions are shown: Bose-Einstein, Fermi-Dirac
and Maxwell-Boltzman. Bose-Einstein statistics apply to
identical bosons (integer spin). Fermi-Dirac to identical fermions
(half integer spin).
Classical statistics are Maxwell-Boltzman applies when the particles
are not identical.
The slider varies the temperature and the
number of particles, M, is a menu. The graph then shows the
population as a function of energy. Shown on the upper right are the
temperature (units of trap energy hbar omega), the energy
that has the maximum population and the population at this energy.
At high temperatures the distributions are much the same. For
low temperatures Bosons form a condensate. These condisates have
been seen in the lab and are the subject of much current research.
At 25K the Bose-Einstein is just starting to form a condensate for
Fermions act just the oppisite and instead avoid each other.
Only one fermion may be in each state. You can see this at low temperatures
as the population goes to the degeneracy of the energy.
White Dwarfs and Neutron Stars are supported by this degeneracy pressure.