Goldstone Bosons in the Gaussian Approximation

The O(N) symmetric scalar quantum field theory with \lambda\Phi^4 interaction is discussed in the Gaussian approximation. It is shown that the Goldstone theorem is fulfilled for arbitrary N.Comment: 7 pages, Late

The Finite Temperature Effective Potential for Local Composite Operators

The method of the effective action for the composite operators $\Phi^2(x)$ and $\Phi^4(x)$ is applied to the termodynamics of the scalar quantum field with $\lambda\Phi^4$ interaction. An expansion of the finite temperature effective potential in powers of $\hbar$ provides successive approximations to the free energy with an effective mass and an effective coupling determined by the gap equations. The numerical results are studied in the space-time of one dimension, when the theory is equivalent to the quantum mechanics of an anharmonic oscillator. The approximations to the free energy show quick convergence to the exact result.Comment: 10 pages, plain Latex, 2 figure

The Effective Action for Local Composite Operators Φ2(x)\Phi^2(x) and Φ4(x)\Phi^4(x)

The generating functionals for the local composite operators, $\Phi^2(x)$ and $\Phi^4(x)$, are used to study excitations in the scalar quantum field theory with $\lambda \Phi^4$ interaction. The effective action for the composite operators is obtained as a series in the Planck constant $\hbar$, and the two- and four-particle propagators are derived. The numerical results are studied in the space-time of one dimension, when the theory is equivalent to the quantum mechanics of an anharmonic oscillator. The effective potential and the poles of the composite propagators are obtained as series in $\hbar$, with effective mass and coupling determined by non-perturbative gap equations. This provides a systematic approximation method for the ground state energy, and for the second and fourth excitations. The results show quick convergence to the exact values, better than that obtained without including the operator $\Phi^4$.Comment: 15 pages, plain Latex, 1 compressed and uuencoded Postscript figur

Optimized perturbation method for the propagation in the anharmonic oscillator potential

The application of the optimized expansion for the quantum-mechanical propagation in the anharmonic potential $\lambda x^4$ is discussed for real and imaginary time. The first order results in the imaginary time formalism provide approximations to the free energy and particle density which agree well with the exact results in the whole range of temperatures.Comment: 13 pages, plain LATEX, 3 compressed and uuencoded Postscript figures, submitted to Phys.Lett.

Two-electron resonances in quasi-one dimensional quantum dots with Gaussian confinement

We consider a quasi one-dimensional quantum dot composed of two Coulombically interacting electrons confined in a Gaussian trap. Apart from bound states, the system exhibits resonances that are related to the autoionization process. Employing the complex-coordinate rotation method, we determine the resonance widths and energies and discuss their dependence on the longitudinal confinement potential and the lateral radius of the quantum dot. The stability properties of the system are discussed.Comment: 12 pages, 7 figure

Optimized Perturbation Methods for the Free Energy of the Anharmonic Oscillator

Two possibile applications of the optimized expansion for the free energy of the quantum-mechanical anharmonic oscillator are discussed. The first method is for the finite temperature effective potential; the second one, for the classical effective potential. The results of both methods show a quick convergence and agree well with the exact free energy in the whole range of temperatures. Postscript figures are available under request to AO email [email protected]: 8 pages, preprin

Exact finite reduced density matrix and von Neumann entropy for the Calogero model

The information content of continuous quantum variables systems is usually studied using a number of well known approximation methods. The approximations are made to obtain the spectrum, eigenfunctions or the reduced density matrices that are essential to calculate the entropy-like quantities that quantify the information. Even in the sparse cases where the spectrum and eigenfunctions are exactly known the entanglement spectrum, {\em i.e.} the spectrum of the reduced density matrices that characterize the problem, must be obtained in an approximate fashion. In this work, we obtain analytically a finite representation of the reduced density matrices of the fundamental state of the N-particle Calogero model for a discrete set of values of the interaction parameter. As a consequence, the exact entanglement spectrum and von Neumann entropy is worked out.Comment: Journal of Physics A (in press

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