System of green functions in solid state physics

Click For Summary

Discussion Overview

The discussion revolves around the formulation of a self-consistent system of Green functions in solid state physics, specifically concerning electrons and phonons within a solid state Hamiltonian framework. Participants explore the implications of their proposed equations and the validity of using Green functions for different quasiparticles.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant proposes a self-consistent system of Green functions for electrons and phonons, questioning the validity of this approach.
  • Another participant agrees that using the free particle propagator for electrons is acceptable but expresses uncertainty about the phonon case, suggesting that the self-energy operator may need to account for deviations from ideal conditions.
  • A different participant raises concerns about whether the proposed system of equations actually exists or if they are independent equations with distinct self-energy contributions for each quasiparticle.
  • One participant recommends using the Born-Oppenheimer approximation to simplify the problem, suggesting a two-stage solution process involving fixed nuclei and harmonic approximations for phonons.
  • A later reply indicates a desire to avoid the Born-Oppenheimer approximation, implying a preference for a more dynamic approach to the system.

Areas of Agreement / Disagreement

Participants express differing views on the formulation of the Green functions and the applicability of the Born-Oppenheimer approximation. There is no consensus on whether the proposed system of equations is valid or if they should be treated independently.

Contextual Notes

Participants mention the need for clarity in notation when referring to different propagators and the potential complexities introduced by interactions and approximations. The discussion highlights the dependence on specific assumptions regarding quasiparticle behavior.

siver
Messages
3
Reaction score
0
Assume we have a solid state hamiltonian, which is ellectrons plus nuclei plus all possible interactions:
H = T_{el} + V_{el-el} + T_{n} + V_{n-n} + V_{n-el}​
Is it wrong to write down a self-consistent system of Green functions for electrons and phonons?
G_{el}=g + gSG_{el}
G_{ph}=g + gSG_{ph}​
S operator does the interraction thing.
Looks fair to me, but I've never seen any articles doing this way.
 
Physics news on Phys.org
If by little 'g' you mean free particle propagator, then it's not wrong --for the electrons. The operator 's' is then the self-energy operator. You can look it up. It's not as obvious to me what little 'g' is for phonons. The typical derivation of phonons has already taken into account effects of electrical interactions in the "spring force" between ions. Maybe you could take the 's' in the case of phonons to represent all the deviations from this ideal case.

p.s. you need to use a different symbol 'g' for electrons and phonons, or you'll get confused.
 
Thanks for reply!

Sure thing g's (free particle propagators) are different for different particle types.
I'm worried if this "system" of two equations eve exist. Maybe they're just independent equations with totally diferent self-patrs for each quasiparticle. And it's pointless to solve them as a system.
 
It's best to use the Born-Oppenheimer approximation. In other words, first consider the locations of the nuclei fixed, and then solve the corresponding electronic problem. This will give you an electronic self-energy that is dependent on the nuclear coordinates. It will also define an effective potential for the nuclear problem according to V(R1, ..., RN) = (total ground state energy when nuclei at coordinates R1, ..., RN). This in turn defines a new problem for the nuclear coordinates. This should be solved in two stages. First stage is harmonic approximation (giving you phonons and little 'g'), and second stage is finding phonon self-energy resulting from anharmonic deviations. Not taking advantage of the Born-Oppenheimer approximation is too ambitious. Only if it fails should you consider chucking it.
 
To avoid BO approx is the main perpose, my system likes to dance. =)
Thanks a lot.
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
3K
Replies
1
Views
5K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 1 ·
Replies
1
Views
3K