A thermodynamic analysis of energy eigenvalues

The use of the thermodynamic “internal energy” U as a tool for characterizing eigenvalue spectra is examined via Monte Carlo studies. We show that for pure and complete spectra, internal energy provides significant separation between individual Gaussian orthogonal ensemble (GOE) and Poisson spectra for spectra with as few as 30-40 levels. We also demonstrate that internal energy is sensitive to the presence of missing or spurious levels in GOE spectra. Comparison of the behavior of U and Δ3 for imperfect spectra shows that the relative variance of U is smaller; therefore, U is less sensitive to experimental limitations affecting the quality of data than is Δ3.