Green functions and projection operators in the semiclassical approximation

K. Möhring, Shimon Levit, Uzy Smilansky

Lee E. Estes, Thomas H. Keil, Lorenzo M. Narducci

Peng Fan, Ke Yang, Kou-Han Ma +1 more

In the equation of motion approach to the two-time Green's functions, conventional Tyablikov-type truncation of the chain of equations is rather arbitrary and apt to violate the analytical structure of Green's functions. Here, we propose a practical way to truncate the equations of motion using operator projection. The partial projection approximation is introduced to evaluate the Liouville matrix. It guarantees the causality of Green's functions, fulfills the time translation invariance and the particle-hole symmetry, and is easy to implement in a computer. To benchmark this method, we study the Anderson impurity model using the operator basis at the level of Lacroix approximation. Improvement over conventional Lacroix approximation is observed. The distribution of Kondo screening in the energy space is studied using this method.

Stephen C. Creagh

The author discusses semiclassical approximations that are adapted to given symmetry classes in quantum mechanics. Arbitrary abelian symmetries and also rotational symmetry are treated. Semiclassical approximations are derived for the projected propagator and energy dependent Green's function associated with a given irreducible representation of the symmetry group. From these they derive trace formulae, analogous to the usual trace formula, that determine the energy levels in a given symmetry class in terms of classical orbits.

Joachim Ankerhold