Bosons at all Temperatures
Most recent answer: 10/22/2007
Q:
Why do bosonic hadrons only act "bosonic" at extremely cold temperatures. i.e. Helium 4. Also, would it be possible to pair fermions into bosons through quantum entanglement?
- Ralph (age 22)
New Mexico
- Ralph (age 22)
New Mexico
A:
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)
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)