Do particles in a system at absolute zero still have kinetic energy?

In summary, at absolute zero in a metal, electrons at the Fermi level still move around at the Fermi velocity, which goes against the classical notion that everything stops at absolute zero. This is due to quantum effects, such as the Pauli principle and zero-point energy, which ensure that even at zero temperature, there is a probability for particles to be in motion. The ground state of the system may have a nonzero probability for particles being in motion, despite being in a state of lowest possible energy.
  • #1
azaharak
152
0
Is it weird that at absolute zero in a metal, electrons at the fermi level still move around at the fermi velocity.

Is the notion that everything stops at absolute zero incorrect?

Thank you
 
Physics news on Phys.org
  • #2
Kinetic energy of free electron: E=p^2/2m in classical mechanics, and E=h^2/2m in quantum mechanics.
Under the classical theory at T=0 V=0 and accordingly E=0. But in quantum mechanics at T=0 electron in a crystal has « Fermi's energy »: E=h^2(3pi^2*n)^(2/3)/2m. As you can see it does not depend on temperature.
Is the notion that everything stops at absolute zero incorrect?
Yes.
I wish success.
 
  • #3
absolute zero and ground state

Yes. The notion that everything comes to a stop is a classical notion and quantum effects will "violate" it. Here, you see the Pauli principle in action. Even without it (i.e. for a system of bosons, or for one isolated particle), you have quantum zero-point energy, ensuring that if you measure the momentum of a particle, there is a probability that it is nonzero even at zero temperature.

The only case where the particles are strictly motionless is for a system of bosons that do not interact, or a single particle, in an infinite geometry without any potentials.

Thus: At T=0, it is not true that particles are at rest. However, it is true that the system (as a whole) is in its ground state, the state of lowest possible energy. (This is by definition, more or less.) But the ground state will typically have a nonzero probability for a particle being in motion!
 
  • #4


AM_Ru said:
Kinetic energy of free electron: E=p^2/2m in classical mechanics, and E=h^2/2m in quantum mechanics.
Under the classical theory at T=0 V=0 and accordingly E=0. But in quantum mechanics at T=0 electron in a crystal has « Fermi's energy »: E=h^2(3pi^2*n)^(2/3)/2m. As you can see it does not depend on temperature.

I have to disagree with all the "content" of that paragraph. 1) The analogy to the energy of the free particle is completely irrelevant at this point. 2) You give a zeroth-order formula for T=0 and impose that this formula is temperature independent. That's trivial and has no significance. To the contrary, the Fermi surface gets smeered out for T>0 because there is a probability distribution in energy.

EmpaDoc said:
Thus: At T=0, it is not true that particles are at rest. However, it is true that the system (as a whole) is in its ground state, the state of lowest possible energy. (This is by definition, more or less.) But the ground state will typically have a nonzero probability for a particle being in motion!

I completely agree with that.
 

What is Fermi Velocity at absolute zero?

Fermi velocity at absolute zero is the maximum speed at which electrons can move in a material at a temperature of absolute zero (0 Kelvin or -273.15 degrees Celsius). It is determined by the material's Fermi energy, which is the highest energy level occupied by electrons at absolute zero.

How is Fermi Velocity related to absolute zero?

The concept of Fermi velocity at absolute zero is based on the Fermi-Dirac distribution, which describes the distribution of electrons in a material at different energy levels. At absolute zero, the distribution reaches its minimum energy state, and the Fermi velocity represents the maximum speed that electrons can move within this distribution.

Is Fermi Velocity at absolute zero the same for all materials?

No, the Fermi velocity at absolute zero can vary depending on the material. It is influenced by the material's density, atomic structure, and other factors. For example, in metals, the Fermi velocity can be several orders of magnitude higher than in insulators.

What is the significance of Fermi Velocity at absolute zero?

Fermi velocity at absolute zero is a fundamental property of materials that affects their electronic and thermal properties. It can also provide information about a material's band structure and electrical conductivity. Additionally, it is a crucial factor in understanding the behavior of electrons in extreme conditions, such as in high magnetic fields or low temperatures.

How is Fermi Velocity at absolute zero measured?

The Fermi velocity at absolute zero can be calculated using various experimental techniques, such as angle-resolved photoemission spectroscopy (ARPES) or tunneling spectroscopy. These methods involve measuring the energy and momentum of electrons in a material and using them to determine the Fermi velocity.

Similar threads

  • Atomic and Condensed Matter
Replies
3
Views
2K
Replies
1
Views
1K
  • Atomic and Condensed Matter
Replies
3
Views
1K
  • Atomic and Condensed Matter
Replies
3
Views
2K
  • Other Physics Topics
Replies
3
Views
1K
  • Quantum Physics
Replies
11
Views
1K
  • Atomic and Condensed Matter
Replies
5
Views
1K
  • Atomic and Condensed Matter
Replies
8
Views
2K
  • Atomic and Condensed Matter
Replies
2
Views
1K
  • Atomic and Condensed Matter
Replies
6
Views
2K
Back
Top