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Amplitude damping with harmonic oscillators

  1. Oct 8, 2009 #1
    Hi

    I am new to this community, so dont beat me up too hard :).

    I have a question about the Hamiltonian when it will simulate the principal system as a harmonic oscillator interacting with the environment which is also an harmonic oscillator (page 291 in "Quantum computation and Quantum information" Nielsen, Chuang).
    Is the communtator [a,b] = 0 ? It seems to me that the operators can't affect each other but I am not sure, should there be a tensor between "a" and "b" in the Hamiltonian?
    Do you have any source to back up your statements?

    Sincerely
    Axel
     
  2. jcsd
  3. Oct 12, 2009 #2
    Okay, I don't have Nielson and Chuang, so I'm not certain what you're talking about, but by conventional notation, it seems that [tex]a[/tex] and [tex]b[/tex] are annihilation operators acting on the system and the environment respectively.

    If that is so, then the [tex][a,b] = 0[/tex] because they act on different Hilbert space. [tex]a[/tex] is an operator in the system Hilbert space; [tex]b[/tex] is an operator in the environment Hilbert space.
     
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