6 research outputs found
Out of equilibrium correlations in the XY chain
We study the transversal XY spin-spin correlations in the non-equilibrium
steady state constructed in \cite{AP03} and prove their spatial exponential
decay close to equilibrium
Non-zero entropy density in the XY chain out of equilibrium
The von Neumann entropy density of a block of n spins is proved to be
non-zero for large n in the non-equilibrium steady state of the XY chain
constructed by coupling a finite cutout of the chain to the two infinite parts
to its left and right which act as thermal reservoirs at different
temperatures. Moreover, the non-equilibrium density is shown to be strictly
greater than the density in thermal equilibrium
Unique Solutions to Hartree-Fock Equations for Closed Shell Atoms
In this paper we study the problem of uniqueness of solutions to the Hartree
and Hartree-Fock equations of atoms. We show, for example, that the
Hartree-Fock ground state of a closed shell atom is unique provided the atomic
number is sufficiently large compared to the number of electrons. More
specifically, a two-electron atom with atomic number has a unique
Hartree-Fock ground state given by two orbitals with opposite spins and
identical spatial wave functions. This statement is wrong for some , which
exhibits a phase segregation.Comment: 18 page
Long time dynamics and coherent states in nonlinear wave equations
We discuss recent progress in finding all coherent states supported by
nonlinear wave equations, their stability and the long time behavior of nearby
solutions.Comment: bases on the authors presentation at 2015 AMMCS-CAIMS Congress, to
appear in Fields Institute Communications: Advances in Applied Mathematics,
Modeling, and Computational Science 201