# About Fermi energy and Fermi temperature

1. May 8, 2008

### shabbir

In classical statistical mechanics, temperature of a system is the measure of its average kinetic energy. In quantum statistical mechanics, Fermi energy corresponds to last filled level at absolute zero and corresponding temperature is the Fermi temperature. Is the Fermi temperature also take some averages into account? What about the temperature of the particles having energy below Fermi energy? Anyone to share me in this regard will be appreciated.

2. May 8, 2008

### lbrits

All the particles are at the same temperature, regardless of their energy. Temperature is a property of a distribution of energies of particles, not a single particle.

Now, once you look at the Fermi-Dirac distribution, and study it for a while, you notice that the combination $$\frac{E_f}{k_B}$$ is important, and this has the right units to be called a temperature. It turns out that the system behaves more and more differently beyond that temperature.

3. May 9, 2008

### shabbir

It means all the Fermions may be at the same temperature simultanously, as it is clear. And Fermi temperature is a purely quantum mechanical concept. So can we say that the Fermi temperature corresponds to ensemble of Fermions in many particle degerate Fermi system? I am bit confused in the sense that Pauli's principle restrict two Fermions to be in the same quantum state, and "temperature" is an average phenomenon, so how to visualize the Fermi temperature?

4. May 12, 2008

### shabbir

It means all the Fermions may be at the same temperature simultanously, as it is clear. And Fermi temperature is a purely quantum mechanical concept. So can we say that the Fermi temperature corresponds to ensemble of Fermions in many particle degerate Fermi system? I am bit confused in the sense that Pauli's principle restrict two Fermions to be in the same quantum state, and "temperature" is an average phenomenon, so how to visualize the Fermi temperature? Can many Fermions (e.g., electrons/positrons) in a many-particle system be at same "Fermi temperature"?

5. Mar 11, 2009

### TheWye

Hi, I just learned this concept of fermi sphere a few months ago as well. What I understand from the term "fermi termperature" is that it is just another way of expressing the fermi energy. It is a purely fictional concept and it just borrows the term "temperature" because it has a linear relationship with Energy:

EF = kB TF

which is similar to the thermodynamics equation

E = n kB T

I don't think it has anything to do with the real physical temperature of the electron itself.

6. Mar 11, 2009

### shabbir

Thanks. But one more thing. The Fermi energy and consequently the Fermi temperature is very large in dense systems e.g. electrons in metals. So At some temperature say 400K, the Fermi pressure is very large as compared with thermal pressure. Can this Fermi pressure drive waves/oscillations due to electronic or ionic motion?

7. Mar 11, 2009

### shabbir

Thanks. But one more thing. The Fermi energy and consequently the Fermi temperature is very large in dense systems e.g. electrons in metals. So for some thermal energy say 0.1eV, the Fermi pressure is still very large as compared with thermal pressure. Can this Fermi pressure drive waves/oscillations due to electronic or ionic motion in a Fermi gas of electrons?