Diophantine equation in the integer quantum hall effect

Click For Summary
SUMMARY

The discussion centers on the relationship between the Diophantine equation and the Integer Quantum Hall Effect (IQHE). Key references include the Thouless article and the Kohmoto article from Physical Review B (1989), which connects the Diophantine equation to the Darboux theorem. The magnetic translation group is also mentioned as a crucial concept, though its connection to the Diophantine equation requires further exploration. A derivation of the Diophantine equation in the context of IQHE is available in a referenced article on JSTOR.

PREREQUISITES
  • Understanding of the Integer Quantum Hall Effect (IQHE)
  • Familiarity with Diophantine equations
  • Knowledge of the Darboux theorem
  • Concepts related to magnetic translation groups
NEXT STEPS
  • Study the derivation of the Diophantine equation in IQHE as presented in the referenced JSTOR article.
  • Research the implications of the Darboux theorem in quantum physics.
  • Explore the properties and applications of the magnetic translation group in condensed matter physics.
  • Review additional literature on the relationship between IQHE and Diophantine equations.
USEFUL FOR

Physicists, particularly those specializing in condensed matter physics, quantum mechanics researchers, and students studying the Integer Quantum Hall Effect.

alex022
Messages
1
Reaction score
0
Hi everybody!

I'm studying the IQHE and I want to understand the rise of the diophantine equation. I read the thouless article but it was no so conclusive.
I've also read the kohmoto article (phys rev B 1989) and he says that that property comes from the darboux theorem but i don't understand why… I've investigated the magnetic translation group but now I cannot do the link with the diophantine equation.

Can you help me?

Thanks a lot!

alex
 
Physics news on Phys.org
Here is a readable derivation of the diophantine equation in IQHE:
http://www.jstor.org/stable/51904?seq=8
See section 5 in particular
 
Last edited by a moderator:
See also the reference they cite for the derivation using magnetic translation group arguement.
 

Similar threads

Graduate Edge state question for a 2-D material and the quantum Hall effect
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Longitudinal resistivity in Integer Quantum Hall Effect
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Rashba-Effect and Intrinsic Spin Hall Effect
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Why the physical meaning of the quantum Hall effect is important
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Quantum Hall Effect and Hall Voltage
  • · Replies 0 ·
Replies
0
Views
1K
Undergrad Hall Conductivity and Rotational Invariance
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Quantum Hall Effect resistivity
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Is the Fractional Quantum Hall Effect an emergent property?
  • · Replies 4 ·
Replies
4
Views
1K
Graduate What Causes the Plateaus and Zeros in the Quantum Hall Effect?
  • · Replies 1 ·
Replies
1
Views
4K
Solid State Books on the Integer Quantum Hall effect
  • · Replies 2 ·
Replies
2
Views
2K