We present a model independent study of the chiral condensate evolution in a hadronic gas, in terms of temperature and baryon chemical potential. The meson-meson interactions are described within Chiral Perturbation Theory and the pion-nucleon interaction by means of Heavy Baryon Chiral Perturbation Theory, both at one loop, and nucleon-nucleon interactions can be safely neglected within our ha...

The KAM theorem for analytic quasi-integrable anisochronous Hamiltonian systems yields that the perturbation expansion (Lindstedt series) for any quasi-periodic solution with Diophantine frequency vector converges. If one studies the Lindstedt series by following a perturbation theory approach, one finds that convergence is ultimately related to the presence of cancellations between contributio...

We consider a model system of two coupled Hopfield neurons, which is described by delay differential equations taking into account the finite signal propagation and processing times. When the delay exceeds a critical value, a limit cycle emerges via a supercritical Hopf bifurcation. First, we calculate its frequency and trajectory perturbatively by applying the Poincaré-Lindstedt method. Then, ...

In this work, we deal with the autonomy issue in the perturbation expansion for the eigenfunctions of a compact Hilbert–Schmidt integral operator. Here, the autonomy points to the perturbation expansion coefficients of the relevant eigenfunction not depending on the perturbation parameter explicitly, but the dependence on this parameter arises from the coordinate change at the zero interval lim...

Using the general argument in Borel resummation of perturbation theory that links the divergent perturbation theory to the nonperturbative effect we argue that the nonperturbative effect associated with the perturbation theory should have a branch cut along the positive real axis in the complex coupling plane. The component in the weak coupling expansion of the nonperturbative amplitude, which ...

1 ∆t ). Furthermore, this nondifferentiability of the trajectories is the source of the Itô calculus [2] in Quantum Mechanics. One expects that the velocity dependent interactions become more important for short time processes. Our goal is to see whether the concept of running coupling constant is meaningful in Quantum Mechanics and it shows an enhancement for velocity dependent interactions at...

Cosmological perturbation theory fails in the new ekpyrotic and cyclic ekpyrotic scenarios, before the scale factor of the Universe reaches zero. As a result, these scenarios do not provide a mechanism for generating the observed curvature perturbation at the bounce. Introduction It is now clear that the dominant cause of large-scale structure in the Universe is a perturbation in the spatial cu...

Cosmological perturbation theory fails in the new ekpyrotic scenario before the scale factor of the Universe reaches zero. As a result, the scenario does not provide a mechanism for generating the observed curvature perturbation at the bounce. Introduction It is now clear that the dominant cause of large-scale structure in the Universe is a perturbation in the spatial curvature [1]. The perturb...

The gravitational evolution of the cosmic one-point probability distribution function (PDF) has been estimated using an analytic approximation that combines gravitational perturbation theory with the Edgeworth expansion around a Gaussian PDF. Despite the remarkable success of the Edgeworth expansion in modeling the weakly non-linear growth of fluctuations around the peak of the cosmic PDF, it f...

We develop a perturbation expansion for the solution of the nonlinear one-dimensional free-electron laser equations. For a monochromatic wave, the radiation field is expanded in a Taylor series having a finite radius of convergence. Analytic continuation using Pade′ approximates yields accurate results well into the saturation regime. We also formulate the perturbation expansion for finite band...