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Homework Help: Reduced density matrix

  1. Sep 15, 2008 #1
    At the thermal equilibrium, the density matrix of a 2 spin-half system is given by:

    [tex]
    \begin{displaymath}
    \mathbf{\rho} =
    \left(\begin{array}{cccc}
    e^{-(1+c)/T} & 0 & 0 & 0\\
    0 & cosh[(1-c)/T] & -sinh[(1-c)/T] & 0\\
    0 & -sinh[(1-c)/T] & cosh[(1-c)/T] & 0\\
    0 & 0 & 0 & e^{-(1+c)/T}
    \end{array}\right)
    \end{displaymath}


    [/tex]

    where c is a parameter.

    How to find the reduced density matrix by tracing out the other spin?
    i.e. [tex]\rho_{1} = tr_{2}\rho[/tex]

    I only know how to find the reduced density matrix for a pure state, say like [tex]\frac{1}{\sqrt{2}}(\left|\downarrow\uparrow> - \left|\uparrow\downarrow> )[/tex]
    But for this given density matrix, i have no idea. Are there any equations that i can use? What's the procedure?
     
  2. jcsd
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