The electron gas with a strong pairing interaction: Three particle correlations and the Thouless instability

We derive simplified Faddeev type equations for the three particle T-matrix which are valid in the Hubbard model where only electrons with opposite spins interact. Using the approximation of dynamical mean field theory these equations are partially solved numerically for the attractive Hubbard model. It is shown that the three particle T-matrix contains a term vanishing $\sim T^2$ at the Thouless (or BCS) instability where the two-particle T-matrix diverges. Based on the three particle term we further derive the low density - strong coupling extension for the two-particle vertex function. We therefore understand our equations as a step towards a systematic low density expansion from the weak coupling BCS theory towards the stronger coupling limit.Comment: 14 pages, 9 figure

Level statistics and localization in a 2D quantum percolation problem

A two dimensional model for quantum percolation with variable tunneling range is studied. For this purpose the Lifshitz model is considered where the disorder enters the Hamiltonian via the nondiagonal elements. We employ a numerical method to analyze the level statistics of this model. It turns out that the level repulsion is strongest around the percolation threshold. As we go away from the maximum level repulsion a crossover from a GOE type behavior to a Poisson like distribution is indicated. The localization properties are calculated by using the sensitivity to boundary conditions and we find a strong crossover from localized to delocalized states.Comment: 4 pages, 4 figure

On the theory of light scattering in molecular liquids

The theory of light scattering for a system of linear molecules with anisotropic polarizabilities is considered. As a starting point for our theory, we express the result of a scattering experiment in VV and VH symmetry as dynamic correlation functions of tensorial densities $\rho_{lm}(q)$ with $l=0$ and $l=2$. $l$, $m$ denote indices of spherical harmonics. To account for all observed hydrodynamic singularities, a generalization of the theory of Schilling and Scheidsteger \cite{schilling97} for these correlation functions is presented, which is capable to describe the light scattering experiments from the liquid regime to the glassy state. As a microscopic theory it fulfills all sum rules contrary to previous {\em phenomenological} theories. We emphasize the importance of the helicity index $m$ for the microscopic theory by showing, that only the existence of $m=1$ components lead to the well known Rytov dip in liquids and to the appearance of transversal sound waves in VH symmetry in the deeply supercooled liquid and the glass. Exact expressions for the phenomenological frequency dependent rotation translation coupling coefficients of previous theories are derived.Comment: 30 pages including 15 figures, submitted to EPJ B, revised version a detailed discussion on the depolarization ratio is added and the discussion on the hydrodynamic analysis is enlarge

Spectral Properties of the Attractive Hubbard Model

Deviations from Fermi liquid behavior are well documented in the normal state of the cuprate superconductors, and some of these differences are possibly related to pre-formed pairs appearing at temperatures above T_c. In order to test these ideas we have investigated the attractive Hubbard model within a self-consistent, conserving ladder approximation. In this version of the theory, no feature is present which can be related to the pseudo gap found in the high-T_c materials. Further, the interactions between two-particle bound states change the physics of the superconducting instability in a profound fashion, and lead to a completely different phenomenology that one predicts based on the non-self-consistent version of the same theory.Comment: 4 pages including 2 figures, to appear in the proceedings of the SNS'9