Convergence of the Linear Delta Expansion in the Critical O(N) Field Theory

The linear delta expansion is applied to the 3-dimensional O(N) scalar field theory at its critical point in a way that is compatible with the large-N limit. For a range of the arbitrary mass parameter, the linear delta expansion for converges, with errors decreasing like a power of the order n in delta. If the principal of minimal sensitivity is used to optimize the convergence rate, the errors seem to decrease exponentially with n.Comment: 26 pages, latex, 8 figure

Electrochemical performances of vitreous materials in the system Li2O–V2O5–P2O5 as electrode for lithium batteries

International audienceGlass composition 25Li2O–50V2O5–25P2O5 has been investigated as a potential material for electrode. Electrical properties as well as electrochemical performances of this glass composition have been characterized and results show a capacity less than 80mAhg−1 when tested in the [3–4.5V] potential window. To the best of our knowledge, this is the first lithiated amorphous material reported as a potential positive electrode material. Glasses, due to their wide available compositions in a given system and their easy processing, pave the way to new type of electrode material

Solvable simulation of a double-well problem in PT symmetric quantum mechanics

Within quantum mechanics which works with parity-pseudo-Hermitian Hamiltonians we study the tunneling in a symmetric double well formed by two delta functions with complex conjugate strengths. The model is exactly solvable and exhibits several interesting features. Besides an amazingly robust absence of any PT symmetry breaking, we observe a quasi-degeneracy of the levels which occurs all over the energy range including the high-energy domain. This pattern is interpreted as a manifestation of certain "quantum beats".Comment: 12 pages incl. 7 figure

On the Divergence of Perturbation Theory. Steps Towards a Convergent Series

The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of the Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum Field Theory. That theorem governs the validity (or lack of it) of the formal manipulations done to generate the perturbative series in the functional integral formalism. The aspects of the perturbative series that need to be modified to obtain a convergent series are presented. Useful tools for a practical implementation of these modifications are developed. Some resummation methods are analyzed in the light of the above mentioned mechanism.Comment: 42 pages, Latex, 4 figure

(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 $F \sim 1/g(m)$ for $m \gg \Lambda$ while $F \sim (m/\Lambda)^\alpha$ for m \lsim \Lambda, $\Lambda$ being the basic scale and $\alpha$ given by renormalization group coefficients. (Borel) convergence holds in a range of $F$ which corresponds to reach unambiguously the strong coupling infrared regime near $m\to 0$, 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 $\delta$ 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 $N$ 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.

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 $SU(2)_L \times SU(2)_R$ and $SU(3)_L \times SU(3)_R$ chiral symmetries in QCD. The method starts with a reorganization of the ordinary perturbation theory with the addition of an arbitrary quark mass $m$. The new perturbative series can be summed to all orders thanks to renormalization group properties, with specific boundary conditions, and advocated analytic continuation in $m$ 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 $M_q$ of the $u,d,s$ quarks; the pion decay constant $F_\pi$; and the quark condensate $$ in terms of the basic QCD scale $\Lambda_{\bar{MS}}$. 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 $F_\pi$ and $M_q$ are roughly in agreement with what is expected from other non-perturbative methods. In contrast we obtain quite a small value of $|< \bar q q >|$ 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.

Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field

We consider the resummation of the perturbation series describing the energy displacement of a hydrogenic bound state in an electric field (known as the Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal power series in the electric field strength. The perturbation series exhibits a rich singularity structure in the Borel plane. Resummation methods are presented which appear to lead to consistent results even in problematic cases where isolated singularities or branch cuts are present on the positive and negative real axis in the Borel plane. Two resummation prescriptions are compared: (i) a variant of the Borel-Pade resummation method, with an additional improvement due to utilization of the leading renormalon poles (for a comprehensive discussion of renormalons see [M. Beneke, Phys. Rep. vol. 317, p. 1 (1999)]), and (ii) a contour-improved combination of the Borel method with an analytic continuation by conformal mapping, and Pade approximations in the conformal variable. The singularity structure in the case of the LoSurdo-Stark effect in the complex Borel plane is shown to be similar to (divergent) perturbative expansions in quantum chromodynamics.Comment: 14 pages, RevTeX, 3 tables, 1 figure; numerical accuracy of results enhanced; one section and one appendix added and some minor changes and additions; to appear in phys. rev.

Gell-Mann - Low Function for QCD in the strong-coupling limit

The Gell-Mann - Low function \beta(g) in QCD (g=g0^2/16\pi^2 where g0 is the coupling constant in the Lagrangian) is shown to behave in the strong-coupling region as \beta_\infty g^\alpha with \alpha\approx -13, \beta_\infty\sim 10^5.Comment: 5 pages, PD

Differential Expression of PGC-1α and Metabolic Sensors Suggest Age-Dependent Induction of Mitochondrial Biogenesis in Friedreich Ataxia Fibroblasts

11 pages, 6 figures. PMID:21687738[PubMed] PMCID: PMC3110204BACKGROUND: Friedreich's ataxia (FRDA) is a mitochondrial rare disease, which molecular origin is associated with defect in the expression of frataxin. The pathological consequences are degeneration of nervous system structures and cardiomyopathy with necrosis and fibrosis, among others. PRINCIPAL FINDINGS: Using FRDA fibroblasts we have characterized the oxidative stress status and mitochondrial biogenesis. We observed deficiency of MnSOD, increased ROS levels and low levels of ATP. Expression of PGC-1α and mtTFA was increased and the active form of the upstream signals p38 MAPK and AMPK in fibroblasts from two patients. Interestingly, the expression of energetic factors correlated with the natural history of disease of the patients, the age when skin biopsy was performed and the size of the GAA expanded alleles. Furthermore, idebenone inhibit mitochondriogenic responses in FRDA cells. CONCLUSIONS: The induction of mitochondrial biogenesis in FRDA may be a consequence of the mitochondrial impairment associated with disease evolution. The increase of ROS and the involvement of the oxidative phosphorylation may be an early event in the cell pathophysiology of frataxin deficiency, whereas increase of mitochondriogenic response might be a later phenomenon associated to the individual age and natural history of the disease, being more evident as the patient age increases and disease evolves. This is a possible explanation of heart disease in FRDA.This work was supported by grants SAF2008-01338, SAF2006-01047 and SAF2009-07063 from the Ministerio de Ciencia e Innovación and financial support from the CIBERER (Biomedical Network Research Center for Rare Diseases). A.G. thanks the Conselleria de Educación of the Generalitat Valenciana for the financial support by grants GVPRE/2008/154. A.B.-A. is the recipient of a JAE-CSIC predoctoral fellowship. The CIBERER is an initiative of the Instituto de Salud Carlos III and INGENIO 2010.Peer reviewe