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Calculate energy level spectra?

  1. Mar 30, 2009 #1
    Recently, I read one book about quantum chaos. In it, random-matrix theory is used to describe the quantum signatures of chaos.
    Firstly, a new set of levels {E’1,E’2,E’3,...} is gained by unfolding the vibrational spectrum {E1,E2,E3,...}:

    [tex]E'_{i+1}=E'_{i}+(2k+1)\frac{E_{i+1}-E_{i}}{E_{j2+1}-E_{j1}}[/tex],
    where [tex]j1=i-k,j2=i+k[/tex]. Let k=3.

    Secondly, the probability distribution of the nearest-neighbor level spacings P(s) of the unfolded spectrum is calculated.

    Here, I want to know how to calculate P(s)?

    In the following, I will show how I calculate the P(s). Maybe it is wrong.
    (1) I unfold the vibrational spectrum {E1,E2,E3,...} and let E’1=0.
    (2) I count how many levels in the energy interval {0-ds},{ds-2ds},{2ds-3ds},…, respectively. Then I obtain P(s).

    I appreciate your help!
     
  2. jcsd
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