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 $x^p$-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 $N$ 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 $\sum a_n \alpha ^n$ 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 $b_0$ (apart from the trivial expansion coefficent $a_0=1/2$). 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 $\epsilon_{\rm F}$ is converging towards any value from an infinite discrete set of energies: ${\epsilon_i}_{i\ge 1}$. If $\epsilon_{\rm F}=\epsilon_i$, 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