I Counting Total Spin for N Two-Level Systems (TLS)

  • I
  • Thread starter Thread starter Haris
  • Start date Start date
  • Tags Tags
    Spin Spin 1/2
Haris
Messages
2
Reaction score
0
TL;DR Summary
I am having considerable trouble understanding the addition of spins. The context in which I am studying this is the Tavis-Cummings Model.
Statement:
"Assume that r and m mean total spin and projection of spin along z, respectively. For N-TLS the total spin (r) can assume N+1 to 1/2 or 0 spin depending on N being even or odd. For a fixed r the value of m varies from +j to -j in integer steps. R is the operator whose eigen-values are r. The basis choice is |r,m>."
Now then, if I intend to make a matrix pretaining to single transitions of the composite system, i align the states with fixed r. For fixed r I have 2m+1 states. When r=N/2 my states are N+1 as simple substitution verifies. However, when r=N/2 -1 the number of states are (N-1)^2. It gets weirder for N/2 -2

Questions:
1) Why is r =N/2 -1 valid as individual spin is half not 1.
2) The counting on main diagonals are pretty confusing. For each irrep of SU(2) there's 2m+1 states and that's fine. But the multiplicity of each state is entirely vague to me.

I have linked the original paper and the figure 1 is where the counting is shown.

1730022772893.png
 

Attachments

Physics news on Phys.org
Correction: its 2r+1 instead of 2m+1
 
I am not sure if this belongs in the biology section, but it appears more of a quantum physics question. Mike Wiest, Associate Professor of Neuroscience at Wellesley College in the US. In 2024 he published the results of an experiment on anaesthesia which purported to point to a role of quantum processes in consciousness; here is a popular exposition: https://neurosciencenews.com/quantum-process-consciousness-27624/ As my expertise in neuroscience doesn't reach up to an ant's ear...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
This is still a great mystery, Einstein called it ""spooky action at a distance" But science and mathematics are full of concepts which at first cause great bafflement but in due course are just accepted. In the case of Quantum Mechanics this gave rise to the saying "Shut up and calculate". In other words, don't try to "understand it" just accept that the mathematics works. The square root of minus one is another example - it does not exist and yet electrical engineers use it to do...

Similar threads

Replies
1
Views
2K
Replies
61
Views
5K
Replies
1
Views
1K
Replies
16
Views
2K
Replies
5
Views
1K
Replies
21
Views
3K
Replies
17
Views
3K
Back
Top