(adsbygoogle = window.adsbygoogle || []).push({}); "straightforward computation..."

Hello. I am reading a paper that discusses moving from a regular [tex] NxN [/tex] dimensional Hilbert space into and [tex]N^2 X N^2[/tex] dimensional Liouville space. The density matrix can be re-written as a [tex]1 X N^2 [/tex]vector by stacking the rows and the Liouvile equation can be re-written as [tex]N^2 X N^2 [/tex]"super-operators" acting on the new density-matrix "vector". The actual form of this super-operator is given by "a straightforward computation" where the field free and interaction Hamiltonians are given by

[tex] H_o=\left(\begin{array}{cc}

-hw & 0 \\

0 & hw

\end{array}\right) [/tex]

and

[tex] H_1=\left(\begin{array}{cc}

0 & d1 \\

d1 & 0

\end{array}\right) [/tex]

The Liouville space super operators describing these in the expanded space are:

[tex] L_o=

\left(\begin{array}{cccc}

0 & 0 & 0 & 0 \\

0 & -hw &0 & 0\\

0 & 0 & hw & 0\\

0 & 0 & 0 & 0

\end{array}\right) [/tex]

and

[tex] L_1=

\left(\begin{array}{cccc}

0 & -d1 & d1 & 0 \\

-d1 & 0 & 0 & d1\\

d1 & 0 & 0 & -d1\\

0 & d1 & -d1 & 0

\end{array}\right) [/tex]

It looks like they're takind a direct product with something, but I can't tell with what or why. They make is sound like it's all just a pretty standard way to write a matrix in a larger space, so if anyone recognizes what's going on here, I'd really happy for your help. Thanks in advance.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Straightforward computation

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**