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Find density matrice at zero and infinity temperature

  1. Jan 16, 2015 #1
    1. The problem statement, all variables and given/known data
    upload_2015-1-16_9-52-47.png

    2. Relevant equations

    https://www.physicsforums.com/attachments/upload_2015-1-15_18-57-56-png.77691/ [Broken]
    Density matrix for a 2 state system is:
    https://www.physicsforums.com/attachments/upload_2015-1-15_19-1-30-png.77694/ [Broken]

    3. The attempt at a solution
    For a 2 finite state system, the matrice density at limit temperature is
    https://www.physicsforums.com/attachments/upload_2015-1-15_18-59-39-png.77692/ [Broken]
    https://www.physicsforums.com/attachments/upload_2015-1-15_18-59-56-png.77693/ [Broken]



    3. The attempt at a solution
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Jan 16, 2015 #2

    DrClaude

    User Avatar

    Staff: Mentor

    You wrote the density matrix in terms of the energy and ##\beta##. What does the finite temperature density matrix in the problems tell you about ##E_1## and ##E_2##?

    Could you give some details about how you reached the solutions you wrote?
     
  4. Jan 16, 2015 #3
    2. Relevant equations

    Density matrix for a 2 state system is:
    upload_2015-1-16_23-10-22.png




    3. The attempt at a solution
    For a 2 finite state system, the matrice density at limit temperature is
    upload_2015-1-16_23-11-35.png

    Evolution of the density matrix
    upload_2015-1-16_23-12-31.png
     
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