Tunneling Transmission Probability: DOS or Velocity?

In summary, the tunneling transmission formula in quantum textbooks only depends on the density of states (DOS) of the regions involved (T(E)=C×DOS1(E)×DOS2(E)). However, the Landauer transmission formula, which does not involve tunneling, also includes the velocity of carriers (T(E)=C′×DOS(E)×v). This raises the question of whether velocity is important in tunneling and if so, which velocity in which region. According to "Introduction to Many-body quantum theory in condensed matter physics" by Bruus et al., the velocity is a factor in the tunneling probability due to the kinetic energy of the tunneling particle.
  • #1
asheg
54
0
In some quantum textbooks [1], the tunneling transmission formula depends only on the density of states of 2 regions (DOS) involved in tunneling. (T(E)=C×DOS1(E)×DOS2(E), where C is constant). However, in Landauer transmission formula (without tunneling) the transmission depends on both DOS and velocity of carriers (T(E)=C′×DOS(E)×v). So I am wondering if velocity is important too? If yes, which velocity in which region?!

[1] For example, see "Introduction to Many-body quantum theory in condensed matter physics", Bruus et al.
 
Physics news on Phys.org
  • #2
The velocity comes in in the form of the kinetic energy of the tunneling particle. So it is explicitly a factor in any tunneling probability for a finite potential.

Zz.
 

1. What is tunneling transmission probability?

Tunneling transmission probability is a concept in quantum mechanics that describes the likelihood of a particle passing through a potential barrier, even when its energy is less than the barrier's height.

2. How is tunneling transmission probability related to DOS?

DOS, or density of states, describes the number of available quantum states at a given energy level. Tunneling transmission probability is related to DOS because it determines the number of quantum states that can contribute to the tunneling process.

3. Is tunneling transmission probability dependent on the material of the potential barrier?

Yes, tunneling transmission probability is highly dependent on the properties of the potential barrier, including its material and thickness. Different materials have different potential energy barriers, which can affect the probability of tunneling.

4. How does the velocity of the tunneling particle affect the transmission probability?

The velocity of the tunneling particle is directly related to its energy. Higher energy particles have a higher velocity and are more likely to tunnel through a potential barrier. Therefore, the velocity of the particle can affect the tunneling transmission probability.

5. Can tunneling transmission probability be measured experimentally?

Yes, tunneling transmission probability can be measured experimentally using techniques such as scanning tunneling microscopy or scanning tunneling spectroscopy. These techniques allow for the observation and measurement of tunneling events and can provide information about the transmission probability.

Similar threads

Phonon density of states and density of states of free electrons
    • Advanced Physics Homework Help
Replies
3
Views
1K
A Microscopic derivation of Josephson effect
    • Atomic and Condensed Matter
Replies
1
Views
859
B Quantum Tunneling different individual transmission probabilities
    • Quantum Physics
Replies
2
Views
889
I The interpretation of probability
    • Quantum Interpretations and Foundations
2
Replies
42
Views
5K
I A question on elasticity from Kittel's Solid State Physics book
    • Atomic and Condensed Matter
Replies
11
Views
2K
A Thermal Properties of the Free Electron Gas: Fermi-Dirac Distribution
    • Atomic and Condensed Matter
Replies
1
Views
2K
Fraction of occupied states (Fermi-Dirac distribution + DOS)
    • Advanced Physics Homework Help
Replies
1
Views
2K
I Density of states in the ideal gas
    • Classical Physics
Replies
2
Views
1K
A Voltage and current waves in a transmission line
    • Electromagnetism
Replies
4
Views
972
FFT of velocity-auto-correlation to get DOS
    • Atomic and Condensed Matter
Replies
1
Views
4K

Hot Threads

Recent Insights

Back
Top