Polarization and degeneracy

In summary, g in photon statistics refers to the internal degeneracy per particle, and in the example of photons with two possible polarization states in three space dimensions, g=2. The number of possible polarization states is equal to the internal degeneracy of the particle because degeneracy refers to different states that have the same energy. This is known as internal degeneracy, as opposed to configurational degeneracy which occurs in systems with a larger number of macroscopic, equivalent configurations. This concept exists in the crossover region between microscopic quantum mechanics and macroscopic degrees of freedom. One example is in ice crystals where the positioning of hydrogen atoms leads to a large number of degenerate ground states. This can also be seen in spin ice
  • #1
jaobyccdee
33
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In photon statistics, g is defined as the internal degeneracy per particle, and the text gives the example that photon have two possible polarization states in three space dimensions, thus g=2. Why is the number of possible polarization equals the internal degeneracy of the particle?
 
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  • #2
Degeneracy just means different states that have the same energy. In most applications, the different polarization states of the photon have the same energy, so that is a degeneracy. I'm not sure why they call it an "internal" degeneracy, I wasn't aware there were any external degeneracies! Perhaps they view spin as something internal, whereas orbital degrees of freedom are external.
 
  • #3
Ken G said:
I'm not sure why they call it an "internal" degeneracy, I wasn't aware there were any external degeneracies!

They are terming it internal degeneracy as opposed to configurational degeneracy. The latter happens when you have a larger number of macroscopic, equivalent configurations. This is interesting for example in systems showing residual configurational entropy like spin ice.
 
  • #4
Cthugha said:
They are terming it internal degeneracy as opposed to configurational degeneracy. The latter happens when you have a larger number of macroscopic, equivalent configurations. This is interesting for example in systems showing residual configurational entropy like spin ice.
OK, so there is a formal meaning to the term, thank you. It sounds like the distinctions live in an interesting crossover region between microscopic quantum mechanics and macroscopic degrees of freedom that nevertheless associate with quantized action.
 
  • #5
Maybe one of the best known examples is ice made from simple water. It is well known that the distance between two Oxygens is roughly 2.76 Angströms, while the OH-bond is roughly 0.95 Angströms. So in ice there are two possible positions for the hydrogen atom along the O-O line: Either at 0.95 Angströms to oxygen atom one and 1.81 Angströms to oxygen atom two or the other way round.

As a consequence in an ice crystal each oxygen atom will have two associated hydrogen atoms at the short distance and two at the long distance, but the exact arrangement is not set as each arrangement fulfilling the above rule leads to the same energy. Therefore you do not get a single ground state when going to 0K, but a huge number of degenerate fround states. You see similar results in spin ice materials like dysprosium titanate.

For some materials the effect can indeed be shown to exist in measurements of the specific heat. However, I suppose, the measurements are no fun.
 
  • #6
That's quite interesting, I did not know that! Counting those states must be an interesting exercise in combinatorics.
 

1. What is polarization?

Polarization is a phenomenon in which the oscillation direction of an electromagnetic wave is restricted to a specific plane. This can occur when the electric field vector of the wave is confined to a single plane, rather than oscillating in all directions.

2. How does polarization occur?

Polarization can occur through various processes, such as reflection, refraction, scattering, and transmission. These processes can alter the direction and orientation of the electric field vector, resulting in polarization.

3. What is degeneracy in physics?

Degeneracy refers to a situation in which multiple quantum states have the same energy level. This can occur in systems with high symmetry, where different states have the same energy due to the symmetrical nature of the system.

4. How is degeneracy related to polarization?

In some cases, degeneracy can cause polarization to occur. For example, in crystals with high symmetry, the degeneracy of energy levels can result in the splitting of the energy levels, leading to polarization of light passing through the crystal.

5. How is polarization and degeneracy studied in science?

Polarization and degeneracy can be studied through various techniques, such as polarimetry, which measures the polarization state of light, and spectroscopy, which can reveal the energy levels and degeneracy of a system. These techniques are valuable in understanding the properties of materials and the behavior of light in different environments.

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