Momentum-dependent and independent intraband relaxation time effects on a non-Markovian (Gaussian line shape) many-body optical gain spectrum are presented. Our theoretical results are compared with experimental data as well as those obtained from a many-body gain model with a conventional Lorentzian line shape function. We show that a Gaussian line shape gain model with a constant intraband relaxation time gives good agreement with experimental gain spectra and the inclusion of k-dependent intraband relaxation time yields slightly improved agreement. In the case of a Lorentzian line shape function, it is found that the inclusion of the k-dependent carrier-carrier scattering in the intraband relaxation time is important to obtain good agreement with the experiment. This is because the Gaussian line shape function is steeper than the Lorentzian for a constant intraband relaxation time. The Gaussian line shape function with a constant intraband relaxation time requires less computational time than that with a k-dependent intraband relaxation time; therefore, it is an efficient model for comparison with experimental data.
The ground-state (GS) properties of the one-dimensional (1D) Hubbard model at half-filling are examined in the presence of a magnetic field using the generalized mean-field (GMF) approach, which includes the spin-density and the electron-hole correlations on an equal footing. The GMF formalism provides insight into both the metal-insulator transition and the transition from itinerant to localized magnetism with applied field. The GMF theory can differentiate the energy gap from the antiferromagnetic order parameter in the presence of a magnetic field. The numerical results for the GS energy, the magnetization, the spin susceptibility, and the number of doubly occupied sites are in good agreement with the exact results over a wide range of U/t and h/t. The calculated h-U phase diagram exhibits a magnetic crossover from itinerant electron-hole pairs to a Bose-Einstein condensate state of local pairs. The overall picture of the magnetic crossover in 1D is found to be similar for the simple case of constant density of states, putting the GMF approach on a firmer basis in two and three dimensions.
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