A new approach to resummation: Parametric Perturbation Theory

Paolo Amore

Home/Archive/arXiv

arXiv · 0705.1166

A new approach to resummation: Parametric Perturbation Theory

Paolo Amore

View original source ↗Read source document ↗Export metadata ↓

Abstract

We present a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are constrained to be linear in a certain (unphysical) parameter. The perturbative expansion is carried out in this parameter and not in the physical coupling (as in ordinary perturbation theory). We show that the method is capable to resum the divergent perturbative series, to {\sl extract} the leading asymptotic (strong coupling) behavior and {\sl predict} with high accuracy the coefficients of the perturbative series.

Explore related subjects

cond-mat.other hep-ph hep-th nucl-th

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Paolo Amore. 2007-05-08. A new approach to resummation: Parametric Perturbation Theory. https://arxiv.org/abs/0705.1166

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Discontinuous-Property Mechanical Metamaterials: A Framework for Discontinuous Lattice Dynamics

Discontinuity, as the extreme limit of nonlinearity, is common in macroscopic continuum systems. This work introduces discontinuous-property mechanical metamaterials (DPMMs) as a prototype for establishing a geometric-mechanics framework for discontinuous lattice systems. We extend band theory to systems with complementary constraints through geometric regularization and analyze modal discontinuities. By analyzing its static, modal, and transient responses, we validated discontinuous stiffness and Poisson's ratio, alongside intense nonlinear wave mixing and mode conversion. A proof-of-concept experiment demonstrates the practical feasibility of implementing DPMMs. This work characterizes discontinuous lattice systems through the intuitive DPMM concept and provides a practical framework to harness sharp transitions in mechanical metamaterials for nonlinear wave manipulation.

cond-mat.other↗

arXiv2026

Magnetic flux ring splitting near a Navier-Stokes singularity

OpenAI reports a forced Navier-Stokes flow that becomes singular in finite time, raising the question of its physical consequences. Magnetic reconnection offers a test through the splitting and merging of flux structures. We use resistive magnetohydrodynamics to simulate a magnetic ring driven by an imposed, regularized flow that reproduces the geometry and scaling of the collapsing core. At the nominal singular time, we remove the imposed drive and allow the system to evolve freely. Reconnections before and after release split the ring into two or more daughter rings through bifurcations of the poloidal flux function, with Lorentz feedback selecting the bifurcation type. Unequal winding by the swirl above and below the midplane produces asymmetric toroidal magnetic stresses, unfolding the kinematic pitchfork-like transition into a fold. For single-island splits, the cusp normal form predicts the asymmetry of the daughter rings without adjustable parameters. Three-dimensional simulations retain the splits and merger, confirming that approach to hydrodynamic blow-up can trigger magnetic restructuring.

cond-mat.other↗

arXiv2026

Non-Hermitian Skin Effect from Radiative Coupling in a Reciprocal Chiral Medium

We show that long-range radiative coupling in a passive chiral medium produces an unusual non-Hermitian skin effect in a chain of dipoles. The skin-mode profile consists of a long-range light-line branch-cut contribution, a non-exponential factor $1/[n(\ln n)^2]$ with $n$ being the site number. Finite-chain calculations show that part of the open-boundary spectrum contracts toward the Bloch spectrum, whereas the number of boundary-localized modes remains extensive. The retarded radiative coupling makes both the real-space profile and the finite-size spectral signatures of boundary localization depart from standard finite-range and pure exponential coupling theory.

cond-mat.other↗