Cooper Pair Formation by Quantizing Brownian Motion

Eqab M. Rabei, Abdul-Wali Ajlouni, H. B. Ghassib

A. O. Bolivar

Hiroshi Nakazawa

Lu, Y.G.

Via the well known chaos decomposition with respect to the multidimensional Brownian motion, we give a possible quantization of a diffusion process (in particular, Brownian motion) on a Riemannian manifold. The quantized diffusion process on Riemannian manifold is a quantum Brownian motion on a Holbert space determined by the momentum algebra.

Hagen M. Kleinert, Sergei V. Shabanov

An exact-diagonalization technique on small clusters is used to study low-lying excitations and superconductivity in the two-dimensional negative-$U$ Hubbard model. We first calculate the Bogoliubov-quasiparticle spectrum, condensation amplitude, and coherence length as functions of the coupling strength $U/t$, thereby working out how the picture of Bogoliubov quasiparticles in the BCS superconductors is affected by increasing the attraction. We then define the Cooper-pair operator as a spatially-extended composite boson and make a variational evaluation of its internal structure. We thereby calculate the single-particle spectral function of the Cooper pair and obtain the dispersion relation for its translational motion. The dynamical density correlation function of the pairs is also calculated. We thus demonstrate the applicability of our numerical method for gaining insight into low-lying excitations of models for the intermediate coupling superconductivity relevant to cuprate materials.