A connection to nuclear physics random matrices

The matrix elements then appear as random variables, and can be allowed the maximum statistical variations consistent with global symmetry requirements imposed on the ensemble of operators. Thus, distributions are only limited by general properties of the system statistical theory does not even attempt to describe the details of a level sequence, but can represent its general features and the degree of fluctuation. 

One must distinguish between this situation and the statistical theories described under the general heading of statistical mechanics in classical statistical mechanics, the laws which govern the evolution of the system are extremely well known, but the path is so complex that it cannot be followed in detail. Here, the number of states is large, but finite, and the randomness arises from an ensemble of possible Hamiltonians. 

This simple argument turns out to be an oversimplification, but the result (10.7) nevertheless turns out to be pretty close to the exact distribution. An extensive discussion of random matrix theory in nuclear physics is given by Mehta [539]. 

Under similar circumstances, particle widths 7 follow the distribution  

An early attempt [543] was made to apply statistical methods to the interpretation of the spectra of complex atoms. For reasons to be discussed in the next section the data are not truly convincing. Another problem to which random matrices are applicable is the electronic structure of metallic clusters when the interlevel spacing becomes larger than the thermal energy, as first shown by Frolich [545] such systems are discussed in chapter 12. 

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