Lowering the Hartree–Fock Minimizer by Electron–Positron Pair Correlation

We prove by a simple computation that a suitable coupling to the positronic sector lowers the energy of the purely electronic minimizer of the electron–positron Hartree–Fock functional.     

On phase segregation in nonlocal two-particle Hartree systems

We prove the phase segregation phenomenon to occur in the ground state solutions of an interacting system of two self-coupled repulsive Hartree equations for large nonlinear and nonlocal interactions. A self-consistent numerical investigation visualizes the approach to this segregated regime.      

Standard components of alternating type centralized by a 4-group

We determine the finite groups possessing a standard subgroup which is the covering group of an alternating group, and whose centralizer is of 2-rank at least 2. The result is one step in the original proof of the classification of the finite simple groups, and presumably also in improvements to that proof. The paper is a modification of the original preprint, which had remained unpublished since the seventies.     

Broken translation invariance in quasifree fermionic correlations out of equilibrium

Using the C^? algebraic scattering approach to study quasifree fermionic systems out of equilibrium in quantum statistical mechanics, we construct the nonequilibrium steady state in the isotropic XY chain whose translation invariance has been broken by a local magnetization and analyze the asymptotic behavior of the expectation value for a class of spatial correlation observables in this state. The effect of the breaking of translation invariance is twofold. Mathematically, the finite rank perturbation not only regularizes the scalar symbol of the invertible Toeplitz operator generating the leading order exponential decay but also gives rise to an additional trace class Hankel operator in the correlation determinant. Physically, in its decay rate, the nonequilibrium steady state exhibits a left mover-right mover structure affected by the scattering at the impurity.