Polarised triplet as initial condition

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Posts: 49
Joined: Tue Jul 13, 2021 8:33 am

Polarised triplet as initial condition

Post by faq_user »

I am a fresh spinach user and I have a question concerning spin polarized states. For the simulations of a spin polarized triplet, I would like to generate a polarized spin state in Liouville space with spherical tensor operators. When I use a S=1 spin and the basis 'sphten-liouv', spinach gives me spin state vectors that have 9 entries.

I am struggeling with the problem what this nine elements in the Liouville space mean. It is clear to me that the first four entries represent the identity operator, the L+, Lz and L- spherical operators. However, I do not know what the other 5 entries mean. To frame it in other words, I would like to know what the Liouville spin state vector representation with spherical tensors of the Zeeman-Hilbert states

0,0,1] and

0,0,0] is in spinach.
Posts: 72
Joined: Mon Mar 29, 2021 4:26 pm

Re: Polarised triplet as initial condition

Post by kuprov »

those five elements are second rank spherical tensor operators. You are receiving a vector of coefficients in front of:

T_1,1; T_1,0; T_1,-1
T_2,2; T_2,1; T_2,0; T_2,-1; T_2,-2

This is very computationally efficient, but indeed may be hard to read.

Switch to 'zeeman-liouv' to make Spinach use the standard Pauli basis, or use sphten2zeeman() to get a projector back into the Pauli basis.
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