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I A question about reduced density matrices

  1. Apr 5, 2016 #1

    naima

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    We have ## \rho ## and a hamiltonian K on ## H_s \otimes H_E##.
    have we [tex] (K \rho)_S \otimes Id_E = K (\rho _S \otimes Id_E)[/tex] ?

    here ## \rho _ s ## and ## (K \rho) _ s ## are the reduced density matrices.
    If P maps an operator O to ##O_S \otimes Id_E##, I have to prove that
    ## PK \rho = KP \rho## for all ##\rho##
     
    Last edited: Apr 5, 2016
  2. jcsd
  3. Apr 5, 2016 #2

    naima

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    This link gave mea this idea:
    ##\partial_t P\rho = i[P\rho, K] = \partial_t (\rho_S \otimes Id_E)
    = \partial_t \rho_S \otimes Id_E = P\partial_t \rho ## as trace and derivation commute.
    ## = iP[\rho, K]##
    So ## PK \rho = KP \rho##
    Is it correct?
     
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