10 research outputs found
Accurate calculation of resonances in multiple-well oscillators
Quantum--mechanical multiple--well oscillators exhibit curious complex
eigenvalues that resemble resonances in models with continuum spectra. We
discuss a method for the accurate calculation of their real and imaginary
parts
A new improved optimization of perturbation theory: applications to the oscillator energy levels and Bose-Einstein critical temperature
Improving perturbation theory via a variational optimization has generally
produced in higher orders an embarrassingly large set of solutions, most of
them unphysical (complex). We introduce an extension of the optimized
perturbation method which leads to a drastic reduction of the number of
acceptable solutions. The properties of this new method are studied and it is
then applied to the calculation of relevant quantities in different
models, such as the anharmonic oscillator energy levels and the critical
Bose-Einstein Condensation temperature shift recently investigated
by various authors. Our present estimates of , incorporating the
most recently available six and seven loop perturbative information, are in
excellent agreement with all the available lattice numerical simulations. This
represents a very substantial improvement over previous treatments.Comment: 9 pages, no figures. v2: minor wording changes in title/abstract, to
appear in Phys.Rev.
The Classical Schrodinger's Equation
A non perturbative numerical method for determining the discrete spectra is
deduced from the classical analogue of the Schrodinger's equation. The energy
eigenvalues coincide with the bifurcation parameters for the classical orbits.Comment: UUEncoded Postscript, 18 pages, 4 figures inserted in tex
Chiral Symmetry Breaking in QCD: A Variational Approach
We develop a "variational mass" expansion approach, recently introduced in
the Gross--Neveu model, to evaluate some of the order parameters of chiral
symmetry breakdown in QCD. The method relies on a reorganization of the usual
perturbation theory with the addition of an "arbitrary quark mass , whose
non-perturbative behaviour is inferred partly from renormalization group
properties, and from analytic continuation in properties. The resulting
ansatz can be optimized, and in the chiral limit we estimate the
dynamical contribution to the "constituent" masses of the light quarks
; the pion decay constant and the quark condensate .Comment: 10 pages, no figures, LaTe
Variational Quark Mass Expansion and the Order Parameters of Chiral Symmetry Breaking
We investigate in some detail a "variational mass" expansion approach,
generalized from a similar construction developed in the Gross-Neveu model, to
evaluate the basic order parameters of the dynamical breaking of the and chiral symmetries in QCD. The
method starts with a reorganization of the ordinary perturbation theory with
the addition of an arbitrary quark mass . The new perturbative series can be
summed to all orders thanks to renormalization group properties, with specific
boundary conditions, and advocated analytic continuation in properties. In
the approximation where the explicit breakdown of the chiral symmetries due to
small current quark masses is neglected, we derive ansatzes for the dynamical
contribution to the "constituent" masses of the quarks; the pion
decay constant ; and the quark condensate in terms of
the basic QCD scale . Those ansatzes are then optimized,
in a sense to be specified, and also explicit symmetry breaking mass terms can
be consistently introduced in the framework. The obtained values of and
are roughly in agreement with what is expected from other
non-perturbative methods. In contrast we obtain quite a small value of within our approach. The possible interpretation of the latter results
is briefly discussed.Comment: 40 pages, LaTex, 2 PS figures. Additions in section 2.2 to better
explain the relation between the current mass and the dynamical mass ansatz.
Minor misprints corrected. Version to appear in Phys. Rev.
(Borel) convergence of the variationally improved mass expansion and the O(N) Gross-Neveu model mass gap
We reconsider in some detail a construction allowing (Borel) convergence of
an alternative perturbative expansion, for specific physical quantities of
asymptotically free models. The usual perturbative expansions (with an explicit
mass dependence) are transmuted into expansions in 1/F, where
for while for m \lsim \Lambda,
being the basic scale and given by renormalization group
coefficients. (Borel) convergence holds in a range of which corresponds to
reach unambiguously the strong coupling infrared regime near , which
can define certain "non-perturbative" quantities, such as the mass gap, from a
resummation of this alternative expansion. Convergence properties can be
further improved, when combined with expansion (variationally improved
perturbation) methods. We illustrate these results by re-evaluating, from
purely perturbative informations, the O(N) Gross-Neveu model mass gap, known
for arbitrary from exact S matrix results. Comparing different levels of
approximations that can be defined within our framework, we find reasonable
agreement with the exact result.Comment: 33 pp., RevTeX4, 6 eps figures. Minor typos, notation and wording
corrections, 2 references added. To appear in Phys. Rev.