- #1
climbon
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I am unsure how to (mathematically) do the partial trace of a density matrix so that I can find the expectation value of an observable.
I am working on a model similar to the Jaynes cummings model. My density matrix is of the form;
[tex]
\rho = [\rho_{11}, \rho_{12}, \rho_{21}, \rho_{22}]
[/tex]
As a 2x2 matrix. My system is a composite system as;
[tex]
H_{A} \otimes H_{B}
[/tex]
I want to find the partial trace over the field so I can use an observable M to find the population inversion of the atom;
[tex]
\rho^{A}(t) = Tr_{F}\rho(t)
[/tex]
That way I can;
[tex]
Tr(M \bullet \rho^{A})
[/tex]
To find the inversion of the atom.
How do i do the trace over the field...I understand the principle but struggling how to do this mathematically??
Thanks
I am working on a model similar to the Jaynes cummings model. My density matrix is of the form;
[tex]
\rho = [\rho_{11}, \rho_{12}, \rho_{21}, \rho_{22}]
[/tex]
As a 2x2 matrix. My system is a composite system as;
[tex]
H_{A} \otimes H_{B}
[/tex]
I want to find the partial trace over the field so I can use an observable M to find the population inversion of the atom;
[tex]
\rho^{A}(t) = Tr_{F}\rho(t)
[/tex]
That way I can;
[tex]
Tr(M \bullet \rho^{A})
[/tex]
To find the inversion of the atom.
How do i do the trace over the field...I understand the principle but struggling how to do this mathematically??
Thanks