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Equilibrium average values

  1. Aug 2, 2010 #1
    Canonical ensemble

    equilibrium average value

    [tex]\left\langle...\right\rangle_0=Q^{-1}Tr(e^{-\beta \hat{H}_0}...)[/tex]

    [tex]\hat{\rho}_0=Q^{-1}e^{-\beta \hat{H}_0}[/tex]

    Grand canonical ensemble

    [tex]\left\langle...\right\rangle_0=Q^{-1}Tr(e^{-\beta (\hat{H}_0-\mu\hat{N})}...)[/tex]

    for example lets say


    Can I say that the equilibrium statistical operator

    [tex]\hat{\rho}_0=Q^{-1}e^{-\beta (\hat{H}_0-\mu\hat{N})}=Q^{-1}e^{-\beta \hat{\mathcal{H}}_0 }[/tex]
  2. jcsd
  3. Aug 2, 2010 #2
    Generally my question is about this ''[tex]0[/tex]'' terms. Do I need to write this?
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