Two-boson Correlations in Various One-dimensional Traps

A one-dimensional system of two trapped bosons which interact through a contact potential is studied using the optimized configuration interaction method. The rapid convergence of the method is demonstrated for trapping potentials of convex and non-convex shapes. The energy spectra, as well as natural orbitals and their occupation numbers are determined in function of the inter-boson interaction strength. Entanglement characteristics are discussed in dependence on the shape of the confining potential.Comment: 5 pages, 3 figure

The Fokker-Planck equation for bistable potential in the optimized expansion

The optimized expansion is used to formulate a systematic approximation scheme to the probability distribution of a stochastic system. The first order approximation for the one-dimensional system driven by noise in an anharmonic potential is shown to agree well with the exact solution of the Fokker-Planck equation. Even for a bistable system the whole period of evolution to equilibrium is correctly described at various noise intensities.Comment: 12 pages, LATEX, 3 Postscript figures compressed an

Quasi-exact solutions for two interacting electrons in two-dimensional anisotropic dots

We present an analysis of the two-dimensional Schrodinger equation for two electrons interacting via Coulombic force and confined in an anizotropic harmonic potential. The separable case of wy = 2wx is studied particularly carefully. The closed-form expressions for bound-state energies and the corresponding eigenfunctions are found at some particular values of wx. For highly-accurate determination of energy levels at other values of wx, we apply an efficient scheme based on the Frobenius expansion.Comment: 11 pages, 4 figure

Comparative study of quantum anharmonic potentials

We perform a study of various anharmonic potentials using a recently developed method. We calculate both the wave functions and the energy eigenvalues for the ground and first excited states of the quartic, sextic and octic potentials with high precision, comparing the results with other techniques available in the literature.Comment: 13 pages, 8 figures and 2 tables; revtex

Perturbative Expansion around the Gaussian Effective Potential of the Fermion Field Theory

We have extended the perturbative expansion method around the Gaussian effective action to the fermionic field theory, by taking the 2-dimensional Gross-Neveu model as an example. We have computed both the zero temperature and the finite temperature effective potentials of the Gross-Neveu model up to the first perturbative correction terms, and have found that the critical temperature, at which dynamically broken symmetry is restored, is significantly improved for small value of the flavour number.Comment: 14pages, no figures, other comments Typographical errors are corrected and new references are adde

Perturbative Expansion around the Gaussian Effective Action: The Background Field Method

We develop a systematic method of the perturbative expansion around the Gaussian effective action based on the background field method. We show, by applying the method to the quantum mechanical anharmonic oscillator problem, that even the first non-trivial correction terms greatly improve the Gaussian approximation.Comment: 16 pages, 3 eps figures, uses RevTeX and epsf. Errors in Table 1 are corrected and new references are adde

Convergence of the Optimized Delta Expansion for the Connected Vacuum Amplitude: Zero Dimensions

Recent proofs of the convergence of the linear delta expansion in zero and in one dimensions have been limited to the analogue of the vacuum generating functional in field theory. In zero dimensions it was shown that with an appropriate, $N$-dependent, choice of an optimizing parameter \l, which is an important feature of the method, the sequence of approximants $Z_N$ tends to $Z$ with an error proportional to ${\rm e}^{-cN}$. In the present paper we establish the convergence of the linear delta expansion for the connected vacuum function $W=\ln Z$. We show that with the same choice of \l the corresponding sequence $W_N$ tends to $W$ with an error proportional to ${\rm e}^{-c\sqrt N}$. The rate of convergence of the latter sequence is governed by the positions of the zeros of $Z_N$.Comment: 20 pages, LaTeX, Imperial/TP/92-93/5

The optimized Rayleigh-Ritz scheme for determining the quantum-mechanical spectrum

The convergence of the Rayleigh-Ritz method with nonlinear parameters optimized through minimization of the trace of the truncated matrix is demonstrated by a comparison with analytically known eigenstates of various quasi-solvable systems. We show that the basis of the harmonic oscillator eigenfunctions with optimized frequency ? enables determination of boundstate energies of one-dimensional oscillators to an arbitrary accuracy, even in the case of highly anharmonic multi-well potentials. The same is true in the spherically symmetric case of V (r) = {\omega}2r2 2 + {\lambda}rk, if k > 0. For spiked oscillators with k < -1, the basis of the pseudoharmonic oscillator eigenfunctions with two parameters ? and {\gamma} is more suitable, and optimization of the latter appears crucial for a precise determination of the spectrum.Comment: 22 pages,8 figure

A Nonperturbative Study of Inverse Symmetry Breaking at High Temperatures

The optimized linear $\delta$-expansion is applied to multi-field $O(N_1) \times O(N_2)$ scalar theories at high temperatures. Using the imaginary time formalism the thermal masses are evaluated perturbatively up to order $\delta^2$ which considers consistently all two-loop contributions. A variational procedure associated with the method generates nonperturbative results which are used to search for parameters values for inverse symmetry breaking (or symmetry nonrestoration) at high temperatures. Our results are compared with the ones obtained by the one-loop perturbative approximation, the gap equation solutions and the renormalization group approach, showing good agreement with the latter method. Apart from strongly supporting inverse symmetry breaking (or symmetry nonrestoration), our results reveal the possibility of other high temperature symmetry breaking patterns for which the last term in the breaking sequence is $O(N_1-1) \times O(N_2-1)$.Comment: 28 pages,5 eps figures (uses epsf), RevTeX. Only a small misprint in Eq. (2.10) and a couple of typos fixe

Chiral and Gluon Condensates at Finite Temperature

We investigate the thermal behaviour of gluon and chiral condensates within an effective Lagrangian of pseudoscalar mesons coupled to a scalar glueball. This Lagrangian mimics the scale and chiral symmetries of QCD. (Submitted to Z. Phys. C)Comment: 20 pages + 7 figures (uuencoded compressed postscript files), University of Regensburg preprint TPR-94-1