The elementary excitation spectrum of a two-component Bose—Einstein condensate in different hyperfine states is obtained by Green's function method. It is found to have two branches. In the long wave-length limit, the two branches of the excitation spectrum are reduced to one phonon excitation and one single-particle excitation. The single-particle one has an energy gap. When the energy gap exists, we study the Landau critical velocity and the depletion of the condensate. With the obtained Green's functions, we calculate the structure factor of a two-component condensate. It is found that the static structure factor comprises only the branch of the phonon excitation and the single-particle excitation makes no contribution to the structure factor.
The quantum dynamics of correlated fermionic or bosonic many-body systems following external excitation can be successfully studied using nonequilibrium Green functions (NEGFs) or reduced density matrix methods. Approximations are introduced via a proper choice of the many-particle self-energy or decoupling of the BBGKY-hierarchy, respectively. These approximations are based on Feynman's diagram approaches or on cluster expansions into single-particle and correlation operators. In a recent paper [E. Schroedter, J.-P. Joost, and M. Bonitz, Condens. Matter Phys. 25, 23401 (2022)] we presented a different approach in which, instead of equations of motion for the many-particle NEGF (or density operators), equations for the correlation functions of fluctuations are analyzed. In particular, we derived the stochastic
GW and polarization approximations that are closely related to the nonequilibrium
GW approximation. Here, we extend this approach to the computation of two-time observables depending on the specific ordering of the underlying operators. In particular, we apply this extension to the calculation of the density correlation function and dynamic structure factor of correlated Hubbard clusters in and out of equilibrium.
An approximate calculation of the excitation spectrum of the Heisenberg linear chain is performed by the Green's-function technique. Apart from the usual transverse Green's function, a longitudinal Green's function is also found useful. The decoupling procedure is not based on the two-sublattice picture, but utilizes the knowledge of known exact results about the ground state of the linear chain and the insight obtained from a model with explicitly known ground state. The equations are solved in a self-consistent manner, and the spectrum, except near the edge of the Brillouin zone, compares well the exact des Cloizeaux-Pearson result. We also provide an expression for the intensity for neutron-scattering studies; this can be checked against measurements on Cu
Cl2\ifmmode\cdot\else\textperiodcentered\fi{}2N(
C5D5) (CPC).