Puzzles about the ''groud state manifold''

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Discussion Overview

The discussion revolves around the concept of the "ground state manifold" in atomic physics, particularly questioning its implications and stability. Participants explore the nature of ground states, degeneracy, and the relationship to symmetry breaking.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions why the term "ground state manifold" is used if the ground state of an atom is usually unique, suggesting it may refer to several nearly degenerate levels.
  • Another participant introduces the concept of spontaneous symmetry breaking using the example of a ferromagnet, arguing that different ground state manifolds correspond to various physical states at the lowest energy level.
  • A different participant counters that the ground state manifold is not related to spontaneous symmetry breaking and suggests it typically consists of finite levels, specifically mentioning a dimension of 5 for the l=2 subspace.
  • One participant notes that the ground state of a hydrogen atom is doubly degenerate due to electron spin, indicating that not all ground states are unique.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between ground state manifolds and symmetry breaking, with no consensus reached on the definitions or implications of these concepts.

Contextual Notes

Some statements rely on specific definitions of terms like "ground state manifold" and "degeneracy," which may not be universally agreed upon. The discussion includes unresolved aspects regarding the stability of the proposed levels.

wdlang
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in atomic physics, sometimes one would encounter the termilogy ''ground state manifold''

my question is, the ground state of an atom is usually unique

How come the ''ground state manifold''?

It means several nearly degenerate level?

are these level stable?
 
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wdlang said:
in atomic physics, sometimes one would encounter the termilogy ''ground state manifold''

my question is, the ground state of an atom is usually unique

How come the ''ground state manifold''?

It means several nearly degenerate level?

are these level stable?

I think you are referring to the spontaneous breakdown of symmetry, right ?

Let's take the example of a ferromagnet. This magnet can be composed out of a gazzillion of iron atoms. Each iron atom will interact with its nearest neighbors by aligning its spin along the direction of the neighbor. This lowers their interaction energy. The lowest possible energy wil be reached once all spins have the same direction. Now, different ground state manifolds means that the system can have different physical ststaes that correspond to the lowest energy state. In our example, the lowest energy corresponds to that system which has all its spins aligned into one direction. But, this direction can be up, down, left, right, in between left and right, etc etc. So there are many possible directions ! Again, what matters is that all spins are aligned ! But the direction of those spins can vary from one system to another. This makes that there are many ground states possible !


marlon
 
no, it has nothing to do with symmetry spontaneous breaking

the manifold usually consists of just finite levels

they may all belong to the l=2 subspace, so the dimension is just 5.

thanks for your interests anyway.
 
wdlang said:
no, it has nothing to do with symmetry spontaneous breaking

the manifold usually consists of just finite levels

they may all belong to the l=2 subspace, so the dimension is just 5.

thanks for your interests anyway.

But then what are you asking about ? Ground state manifold just means ground state energy level, that's it.

marlon
 
hehe, i watched the movies of you on youtube

you are a handsome guy!
 
wdlang said:
in atomic physics, sometimes one would encounter the termilogy ''ground state manifold''

my question is, the ground state of an atom is usually unique

well... for example, the ground state of a H-atom is doubly degenerate due to electron spin.
 

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