126 research outputs found
Variational Perturbation Theory for the Ground-State Wave Function
We evaluate perturbatively the density matrix in the low-temperature limit
and thus the ground-state wave function of the anharmonic oscillator up to
second order in the coupling constant. We then employ Kleinert's variational
perturbation theory to determine the ground-state wave function for all
coupling strengths.Comment: The article is a contribution to the book "Fluctuating Paths and
Fields - Dedicated to Hagen Kleinert on the Occasion of His 60th Birthday",
Eds. Wolfhard Janke, Axel Pelster, Hans-Juergen Schmidt, and Michael Bachmann
(World Scientific, Singapore, 2001), p. 315-32
The Highest-Derivative Version of Variational Perturbation Theory
We systematically investigate different versions of variational perturbation
theory by forcing not only the first or second but also higher derivatives of
the approximant with respect to the variational parameter to vanish. The choice
of the highest derivative version turns out to be the most successful one for
approximating the ground-state energy of the anharmonic oscillator. It is
therefore used to determine the critical exponent alpha of the specific heat in
superfluid 4He in agreement with the value measured in recent space shuttle
experiments.Comment: The article is a contribution to the book "Fluctuating Paths and
Fields - Dedicated to Hagen Kleinert on the Occasion of His 60th Birthday",
Eds. Wolfhard Janke, Axel Pelster, Hans-Juergen Schmidt, and Michael Bachmann
(World Scientific, Singapore, 2001), p. 347-36
A theory of finite-temperature Bose-Einstein condensates in neutron stars
We investigate the possible occurrence of a Bose-Einstein condensed phase of
matter within neutron stars due to the formation of Cooper pairs among the
superfluid neutrons. To this end we study the condensation of bosonic particles
under the influence of both a short-range contact and a long-range
gravitational interaction in the framework of a Hartree-Fock theory. We
consider a finite-temperature scenario, generalizing existing approaches, and
derive macroscopic and astrophysically relevant quantities like a mass limit
for neutron stars.Comment: 21 pages, 9 figures; replaced after publication with additional
comment
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