32 research outputs found
Entanglement entropies in the ground states of helium-like atoms
We examine the entanglement in the ground states of helium and helium-like
ions using an original Hylleraas expansion. The von Neumann and linear
entropies of the reduced density matrix are accurately computed by performing
the Schmidt decomposition of the S singlet spatial wavefunctions. The results
presented are more accurate than currently available in published literature.Comment: 6 pages, 1 figur
A Variational Expansion for the Free Energy of a Bosonic System
In this paper, a variational perturbation scheme for nonrelativistic
many-Fermion systems is generalized to a Bosonic system. By calculating the
free energy of an anharmonic oscillator model, we investigated this variational
expansion scheme for its efficiency. Using the modified Feynman rules for the
diagrams, we obtained the analytical expression of the free energy up to the
fourth order. Our numerical results at various orders are compared with the
exact and other relevant results.Comment: 9 pages, 3 EPS figures. With a few typo errors corrected. to appear
in J. Phys.
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
Gaussian Effective Potential and the Coleman's normal-ordering Prescription : the Functional Integral Formalism
For a class of system, the potential of whose Bosonic Hamiltonian has a
Fourier representation in the sense of tempered distributions, we calculate the
Gaussian effective potential within the framework of functional integral
formalism. We show that the Coleman's normal-ordering prescription can be
formally generalized to the functional integral formalism.Comment: 6 pages, revtex; With derivation details and an example added. To
appear in J. Phys.
Mass generation without phase coherence in the Chiral Gross-Neveu Model at finite temperature and small N in 2+1 dimensions
The chiral Gross-Neveu model is one of the most popular toy models for QCD.
In the past, it has been studied in detail in the large-N limit. In this paper
we study its small-N behavior at finite temperature in 2+1 dimensions. We show
that at small N the phase diagram of this model is {\it principally} different
from its behavior at . We show that for a small number of
fermions the model possesses two characteristic temperatures and
. That is, at small N, along with a quasiordered phase the
system possesses a very large region of precursor fluctuations
which disappear only at a temperature , substantially higher than the
temperature of Kosterlitz-Thouless transition.Comment: a factor 2 corrected. An extended discussion of similarities and
differences of low-N behavior of the chiral GN model and various models of
superconductivity is currently in preparation and will be presented in
additional articl
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
Variational perturbation approach to the Coulomb electron gas
The efficiency of the variational perturbation theory [Phys. Rev. C {\bf 62},
045503 (2000)] formulated recently for many-particle systems is examined by
calculating the ground state correlation energy of the 3D electron gas with the
Coulomb interaction. The perturbation beyond a variational result can be
carried out systematically by the modified Wick's theorem which defines a
contraction rule about the renormalized perturbation. Utilizing the theorem,
variational ring diagrams of the electron gas are summed up. As a result, the
correlation energy is found to be much closer to the result of the Green's
function Monte Carlo calculation than that of the conventional ring
approximation is.Comment: 4 pages, 3 figure
Sine-Gordon Expectation Values of Exponential Fields With Variational Perturbation Theory
In this paper, expectation values of exponential fields in the 2-dimensional
Euclidean sine-Gordon field theory are calculated with variational perturbation
approach up to the second order. Our numerical analysis indicates that for not
large values of the exponential-field parameter , our results agree very
well with the exact formula conjectured by Lukyanov and Zamolodchikov in Nucl.
Phys. B 493, 571 (1997).Comment: only abbreviated the original, 12 pages, 2 EPS figures, to be
published in Phys. Lett.
QCD Running Coupling Constant in the Timelike Region
By using a non-perturbative expansion and the dispersion relation for the
Adler --function we propose a new method for constructing the QCD effective
coupling constant in the timelike region.Comment: LaTeX, 11 pages, 4 figure