Abstract
Embedded Gaussian orthogonal ensemble of random matrices for spinless fermion systems generated by random two-body interactions [EGOE(2)] is defined and a method for its construction is described. One-point function giving eigenvalue density and some aspects of the two-point function that generates level fluctuations for the more general EGOE(k), generated by a random k-body interaction, are derived in detail using binary correlation approximation (BCA). In the dilute limit, one-point function is a Gaussian and as number of particles m increases from m=k, eigenvalue densities exhibit semi-circle to Gaussian transition with m=2k being the transition point. Secondly, EGOE(k) exhibits average-fluctuation separation as m increases and also non-zero cross correlations between spectra with different particle numbers. In addition, asymptotic form of the transition strength densities, that are also two-point functions, generated by a transition operator, is established using BCA to be a bivariate Gaussian. Then, smoothed transition strength sums, being marginal densities divided by the state density, will be ratio of two Gaussians. Thus, EGOE differs from GOE both in one- and two-point functions.
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Kota, V.K.B. (2014). Embedded GOE for Spinless Fermion Systems: EGOE(2) and EGOE(k). In: Embedded Random Matrix Ensembles in Quantum Physics. Lecture Notes in Physics, vol 884. Springer, Cham. https://doi.org/10.1007/978-3-319-04567-2_4
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DOI: https://doi.org/10.1007/978-3-319-04567-2_4
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