The optical conductivity (OC) of cuprates is studied theoretically in the low density limit of the t-t-J-Holstein model. By developing a limited phonon basis exact diagonalization (LPBED) method capable of treating the lattice of largest size 4x4 eve
r considered, we are able to discern fine features of the mid-infrared (MIR) part of the OC revealing three-peak structure. The two lowest peaks are observed in experiments and the highest one is tacitly resolved in moderately doped cuprates. Comparison of OC with the results of semianalytic approaches and detailed analysis of the calculated isotope effect indicate that the middle-energy MIR peak is of mostly magnetic origin while the lowest MIR band originates from the scattering of holes by phonons.
We discuss the zero-temperature hydrodynamics equations of bosonic and fermionic superfluids and their connection with generalized Gross-Pitaevskii and Ginzburg-Landau equations through a single superfluid nonlinear Schrodinger equation.
We study vortical states in a Bose-Einstein condensate (BEC) filling a cigar-shaped trap. An effective one-dimensional (1D) nonpolynomial Schroedinger equation (NPSE) is derived in this setting, for the models with both repulsive and attractive inter
-atomic interactions. Analytical formulas for the density profiles are obtained from the NPSE in the case of self-repulsion within the Thomas-Fermi approximation, and in the case of the self-attraction as exact solutions (bright solitons). A crucially important ingredient of the analysis is the comparison of these predictions with direct numerical solutions for the vortex states in the underlying 3D Gross-Pitaevskii equation (GPE). The comparison demonstrates that the NPSE provides for a very accurate approximation, in all the cases, including the prediction of the stability of the bright solitons and collapse threshold for them. In addition to the straight cigar-shaped trap, we also consider a torus-shaped configuration. In that case, we find a threshold for the transition from the axially uniform state, with the transverse intrinsic vorticity, to a symmetry-breaking pattern, due to the instability in the self-attractive BEC filling the circular trap.
