Well, bosons act like bosons at all temperatures. I'm surprised you
used the word "hadrons" in this context -- there are indeed bosonic
hadrons, but I cannot think of any stable ones. Hadrons are things made
up of quarks and gluons. Protons and neutrons are the usual hadrons
we're most familiar with, but they're fermions (they have half a unit
of spin).
A Helium 4 atom is, collectively, a boson, even though it is a
bound state of several distinct pieces. It's not a hadron because it
has two real electrons. We particle physicists are even reluctant to
call a Helium 4 nucleus a hadron, as we prefer the name nucleus.
Anyhow, Helium 4 becomes superfluid at about 2.2 Kelvin, in a
transition that has lots to do with the fact that Helium 4 is a boson
(Helium 3 becomes a superfluid too, but at a much lower temperature,
and does so because the Helium 3 atoms form pairs). The reason that
gases of fermions and bosons act so differently at low temperatures
comes from the Pauli exclusion principle and the occupation of states.
At very low temperatures, the particles in the system are found in the
lowest energy states they can get themselves into. Two fermions cannot
occupy the same quantum state because of the Pauli exclusion principle.
So the states fill up to a maximum energy when all the particles have
found places, and this maximum is called the Fermi energy. At higher
temperatures, particles can occupy excited states above the Fermi
energy, but at low temperatures they all settle into their lowest
possible states.
Bosons don't obey the Pauli exclusion principle -- you can go on
and put as many as you like into the same quantum state. At low
temperatures, this is exactly what happens, at least for
non-interacting bosons -- the lowest possible quantum state gets a big
fraction of the particles in it. The quantum state is also spread out
over a macroscopic space, making the macroscopic properties of
condensates of bosons very interesting. Search the web for
"Bose-Einstein Condensate" and also "Superfluid" for more good info.
But these properties also affect fermions and bosons at higher
temperatures too. Atomic shells keep their structures to very very high
temperatures, and the mobile electrons in metals fill up a sea of
states at room temperature that is only a tiny bit different and only
at the very surface, from their behavior at absolute zero.
Bosonic hadrons (I'm not sure this is really what you wanted to
ask, but I'll answer it anyway) live for a short amount of time after
they are produced in high-energy particle collisions. Examples are
pions, kaons, rho and omega mesons, etas, D mesons and B mesons, each
with its own special properties. Pions and kaons live long enough to
fly through detectors and leave trails of ionized gas behind them (if
the detector is made out of a gas that's easily ionized). We have
studied these in high-energy reactions and have found that pions tend
to "clump up" in energy and angle space -- they are produced in
correlated bunches due to the fact that they are bosons and prefer to
occupy the same quantum state. This effect is called "Bose-Einstein
Correlation" and has been well documented in very high-energy
interactions.
Fermions pair up to form bosons, and the quantum description of it
requires a wavefunction that depends simultaneously on the coordinates
and spins of both of the fermions. I guess any multiparticle system
with coherence between particle states is "entangled", although we
don't usually use that word when talking about fermion pairing.
Tom (w. Mike)
(published on 10/22/2007)
