82 research outputs found
Scaling property of variational perturbation expansion for general anharmonic oscillator
We prove a powerful scaling property for the extremality condition in the
recently developed variational perturbation theory which converts divergent
perturbation expansions into exponentially fast convergent ones. The proof is
given for the energy eigenvalues of an anharmonic oscillator with an arbitrary
-potential. The scaling property greatly increases the accuracy of the
results
Thermodynamics of a weakly interacting Bose-Einstein gas
The one-loop effective potential for non-relativistic bosons with a delta
function repulsive potential is calculated for a given chemical potential using
functional methods. After renormalization and at zero temperature it reproduces
the standard ground state energy and pressureas function of the particle
density. At finite temperatures it is found necessary to include ring
corrections to the one-loop result in order to satisfy the Goldstone theorem.
It is natural to introduce an effective chemical potential directly related to
the order parameter and which uniformly decreases with increasing temperatures.
This is in contrast to the the ordinary chemical potential which peaks at the
critical temperature. The resulting thermodynamics in the condensed phase at
very low temperatures is found to be the same as in the Bogoliubov
approximation where the degrees of freedom are given by the Goldstone bosons.
At higher temperatures the ring corrections dominate and result in a critical
temperature unaffected by the interaction.Comment: 39 pages, 9 figures, picTex, submitted to Annals of Physics.
Discussions on renormalization and off-diagonal self energies are made
clearer in this version. A short derivation of the non-relativistic limit is
adde
Density and Pair Correlation Function of Confined Identical Particles: the Bose-Einstein Case
Two basic correlation functions are calculated for a model of
harmonically interacting identical particles in a parabolic potential well. The
density and the pair correlation function of the model are investigated for the
boson case. The dependence of these static response properties on the complete
range of the temperature and of the number of particles is obtained. The
calculation technique is based on the path integral approach of symmetrized
density matrices for identical particles in a parabolic confining well.Comment: 8 pages (REVTEX) + 6 figures (postscript
Dependence of Variational Perturbation Expansions on Strong-Coupling Behavior. Inapplicability of delta-Expansion to Field Theory
We show that in applications of variational theory to quantum field theory it
is essential to account for the correct Wegner exponent omega governing the
approach to the strong-coupling, or scaling limit. Otherwise the procedure
either does not converge at all or to the wrong limit. This invalidates all
papers applying the so-called delta-expansion to quantum field theory.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper (including all PS fonts) at
http://www.physik.fu-berlin.de/~kleinert/34
Variational Interpolation Algorithm between Weak- and Strong-Coupling Expansions
For many physical quantities, theory supplies weak- and strong-coupling
expansions of the types and \alpha ^p\sum b_n
(\alpha^{-2/q) ^n, respectively. Either or both of these may have a zero
radius of convergence. We present a simple interpolation algorithm which
rapidly converges for an increasing number of known expansion coefficients. The
accuracy is illustrated by calculating the ground state energies of the
anharmonic oscillator using only the leading large-order coefficient
(apart from the trivial expansion coefficent ). The errors are less
than 0.5 for all g. The algorithm is applied to find energy and mass of the
Fr\"ohlich-Feynman polaron. Our mass is quite different from Feynman's
variational approach.Comment: PostScript, http://www.physik.fu-berlin.de/kleinert.htm
Electrical Resistivity Anisotropy from Self-Organized One-Dimensionality in High-Temperature Superconductors
We investigate the manifestation of the stripes in the in-plane resistivity
anisotropy in untwinned single crystals of La_{2-x}Sr_{x}CuO_{4} (x = 0.02 -
0.04) and YBa_{2}Cu_{3}O_{y} (y = 6.35 - 7.0). It is found that both systems
show strongly temperature-dependent in-plane anisotropy in the lightly
hole-doped region and that the anisotropy in YBa_{2}Cu_{3}O_{y} grows with
decreasing y below about 6.60 despite the decreasing orthorhombicity, which
gives most direct evidence that electrons self-organize into a macroscopically
anisotropic state. The transport is found to be easier along the direction of
the spin stripes already reported, demonstrating that the stripes are
intrinsically conducting in cuprates.Comment: 5 pages, 4 figures (including one color figure), final version
accepted for publication in Phys. Rev. Let
Correlations in a Confined gas of Harmonically Interacting Spin-Polarized Fermions
For a fermion gas with equally spaced energy levels, the density and the pair
correlation function are obtained. The derivation is based on the path integral
approach for identical particles and the inversion of the generating functions
for both static responses. The density and the pair correlation function are
evaluated explicitly in the ground state of a confined fermion system with a
number of particles ranging from 1 to 220 and filling the Fermi level
completely.Comment: 11 REVTEX pages, 3 postscript figures. Accepted for publication in
Phys. Rev. E, Vol. 58 (August 1, 1998
Dimensionality effects in restricted bosonic and fermionic systems
The phenomenon of Bose-like condensation, the continuous change of the
dimensionality of the particle distribution as a consequence of freezing out of
one or more degrees of freedom in the low particle density limit, is
investigated theoretically in the case of closed systems of massive bosons and
fermions, described by general single-particle hamiltonians. This phenomenon is
similar for both types of particles and, for some energy spectra, exhibits
features specific to multiple-step Bose-Einstein condensation, for instance the
appearance of maxima in the specific heat.
In the case of fermions, as the particle density increases, another
phenomenon is also observed. For certain types of single particle hamiltonians,
the specific heat is approaching asymptotically a divergent behavior at zero
temperature, as the Fermi energy is converging towards any
value from an infinite discrete set of energies: . If
, for any i, the specific heat is divergent at T=0
just in infinite systems, whereas for any finite system the specific heat
approaches zero at low enough temperatures. The results are particularized for
particles trapped inside parallelepipedic boxes and harmonic potentials.
PACS numbers: 05.30.Ch, 64.90.+b, 05.30.Fk, 05.30.JpComment: 7 pages, 3 figures (included
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