Abstract
Embedded GOE generated by random two-body interactions in the presence of a one-body mean-field [called EGOE(1+2)] for spinless fermion systems is introduced and its construction follows easily from that of EGOE(2). In the limiting situation with the two-body interaction much stronger than the mean-field, EGOE(1+2) reduces to EGOE(2). Examining eigenvalue density, level fluctuations, strength functions, information and occupancy entropies as a function of the interaction strength λ (expressed in the units of the average spacing of the energies of the mean-field one-particle states), it is shown numerically that the ensemble generates three transition or chaos markers. They correspond to Poisson to GOE transition in level fluctuations, Breit-Wigner to Gaussian transition in strength functions and the third marker defining a region of thermalization. Using unitary decomposition and trace propagation on one hand and perturbation theory on the other, parametric dependence of the three chaos markers are determined. Also derived are formulas for number of principal components (NPC), information entropy and occupancy entropy.
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Kota, V.K.B. (2014). Random Two-Body Interactions in Presence of Mean-Field: EGOE(1+2). 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_5
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DOI: https://doi.org/10.1007/978-3-319-04567-2_5
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