20 research outputs found
Implicit Density Functional Theory
A fermion ground state energy functional is set up in terms of particle
density, relative pair density, and kinetic energy tensor density. It satisfies
a minimum principle if constrained by a complete set of compatibility
conditions. A partial set, which thereby results in a lower bound energy under
minimization, is obtained from the solution of model systems, as well as a
small number of exact sum rules. Prototypical application is made to several
one-dimensional spinless non-interacting models. The effectiveness of "atomic"
constraints on model "molecules" is observed, as well as the structure of
systems with only finitely many bound states.Comment: 9 pages, 4 figure
Quasiparticle Effective Mass for the Two- and Three-Dimensional Electron Gas
We calculate the quasiparticle effective mass for the electron gas in two and
three dimensions in the metallic region. We employ the single particle
scattering potential coming from the Sj\"{o}lander-Stott theory and enforce the
Friedel sum rule by adjusting the effective electron mass in a scattering
calculation. In 3D our effective mass is a monotonically decreasing function of
throughout the whole metallic domain, as implied by the most recent
numerical results. In 2D we obtain reasonable agreement with the experimental
data, as well as with other calculations based on the Fermi liquid theory. We
also present results of a variety of different treatments for the effective
mass in 2D and 3D.Comment: 12 pages, 2 figure
Phase space reduction of the one-dimensional Fokker-Planck (Kramers) equation
A pointlike particle of finite mass m, moving in a one-dimensional viscous
environment and biased by a spatially dependent force, is considered. We
present a rigorous mapping of the Fokker-Planck equation, which determines
evolution of the particle density in phase space, onto the spatial coordinate
x. The result is the Smoluchowski equation, valid in the overdamped limit,
m->0, with a series of corrections expanded in powers of m. They are determined
unambiguously within the recurrence mapping procedure. The method and the
results are interpreted on the simplest model with no field and on the damped
harmonic oscillator.Comment: 13 pages, 1 figur