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Partial trace of density matrix

  1. Aug 2, 2012 #1
    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
     
  2. jcsd
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