Fermi Surface and Orthogonality Catastrophe

Click For Summary
SUMMARY

The discussion centers on the concept of the discontinuous jump in the occupation number, denoted as Z, in the context of Fermi surfaces and the orthogonality catastrophe. Z is defined as the probability of the system transitioning to an N+1 or N-1 ground state upon the addition or removal of an electron, respectively. This relationship is derived from equation 8.123 in the referenced text, "Quantum Theory of the Electron Liquid" by Giuliani and Vignale. Participants seek clarification on the logical connection between equation 8.123 and the definition of Z.

PREREQUISITES
  • Understanding of Fermi surfaces in solid-state physics
  • Familiarity with quantum mechanics, specifically occupation numbers
  • Knowledge of the orthogonality catastrophe concept
  • Ability to interpret mathematical expressions in quantum field theory
NEXT STEPS
  • Study the derivation of equation 8.123 in "Quantum Theory of the Electron Liquid"
  • Explore the implications of the orthogonality catastrophe in many-body physics
  • Learn about the role of occupation numbers in quantum statistical mechanics
  • Investigate applications of Fermi surface theory in condensed matter physics
USEFUL FOR

Physicists, particularly those specializing in condensed matter physics, quantum mechanics students, and researchers interested in many-body systems and Fermi surface phenomena.

Morberticus
Messages
82
Reaction score
0
I am reading section 8.5.1 of http://f3.tiera.ru/2/P_Physics/PS_Solid%20state/Giuliani%20G.,%20Vignale%20G.%20Quantum%20theory%20of%20the%20electron%20liquid%20%28CUP,%202005%29%28ISBN%200521821126%29%28799s%29_PS_.pdf (page 442 of the book, page 465 of the pdf). The author claims the discontinuous jump in the occupation number is of size Z, where

Z = |\langle 0,N+1|a^\dagger |0,N\rangle|^2 = |\langle 0,N-1|a |0,N\rangle|^2

I.e. Z is the probability that the system will be in an N+1 (N-1) ground state after an electron is added (removed). They say this follows from equation 8.123 but I don't find it obvious how. Is there an easy logical path from equation 8.123 to the above relation?
 
Last edited by a moderator:
Physics news on Phys.org
I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
 
post equation 8.123 for us