Lattice time-dependent correlated two-electron system approach to scattering problems

Steven Allan Kivelson

Yu-Liang Liu

With the eigenfunctional theory, we study the correlation of the local electrons in the Kondo lattice model, and give a general formulation to calculate the correlation functions of the local electrons where it ends in order to calculate the partition function of the conduction electrons with time-dependent external potentials. This formulation may be very useful to study the low-energy physical property of the Kondo lattice model by numerical simulations, especially by the quantum Monte Carlo method. In order to justify this formulation, we apply it for one and two magnetic impurities scattering problems in the continuum limit, and obtain reliable results that are in agreement with previous exact results.

A. S. Alexandrov, Sergei V. Traven, P. E. Kornilovitch

The problem of two electrons on a one-dimensional (1D) lattice is solved for the case when the lattice unit cell contains two unequivalent sites a and b with two corresponding electron-electron correlation potentials: attractive U a and repulsive U b . It is shown, that the kinematics of the electron-electron scattering in such a system are remarkably different from those of the ordinary 1D Hubbard model because of the presence of the Umklapp processes. Analytical properties of the S-matrix are studied. Ground state properties and excitation spectrum are analyzed as functions of U a and U b .

Andrea Di Ciolo, Adolfo Avella

E. C. Goldberg, Mario C. G. Passeggi

The Green function formalism introduced by Keldysh for irreversible processes is applied to the calculation of the time-dependent charge exchange probabilities in scattering problems. Considering the initial state of two non-interacting subsystems described by an independent particle model, their interaction is taken in a first stage, as evolving in time according to a time-dependent Hartree - Fock (TDHF) scheme. The equations of motion for the two-times Green functions are subsequently obtained in Dyson-like form by including the residual electronic correlations expanded perturbatively up to second order. It is shown that, by solving these equations of motion, this in turn allows one to calculate the two-particle correlation functions at equal times, as required to describe the fractions of charge in each subsystem. This procedure contrasts with that of considering expectation values of the correlation functions taken between the corrected TDHF state up to an equivalent order in the perturbation. In order to test the advantages of this method we have applied this scheme to the scattering of an atom from a three-substrate atom chain described by an Anderson Hamiltonian, where comparisons with exact solutions can be easily established. We found that, in this case, the fractions of charges carried by the scattered particle obtained with our proposal compare fairly well with exact results, within an ample range of parameter selection.

Philip A. E. Murgatroyd