A test on the numerical accuracy of the semiclassical approximation as a function of the principal quantum number has been performed for the Pullen– Edmonds model, a two–dimensional, non–integrable, scaling invariant perturbation of the resonant harmonic oscillator. A perturbative interpretation is obtained of the recently observed phenomenon of the accuracy decrease on the approximation of ind...

We introduce a new method, namely, the Optimal Iteration Perturbation Method OIPM , to solve nonlinear differential equations of oscillators with cubic and harmonic restoring force. We illustrate that OIPM is very effective and convenient and does not require linearization or small perturbation. Contrary to conventional methods, in OIPM, only one iteration leads to high accuracy of the solution...

Four-point functions of gauge-invariant operators in D = 4, N = 4 supersymmetric Yang-Mills theory are studied using N = 2 harmonic superspace perturbation theory. The results are expressed in terms of differential operators acting on a scalar two loop integral. The leading singular behaviour is obtained in the limit that two of the points approach one another. We find logarithmic singularities...

The stability, instability, and bifurcation behaviour of a nonlinear autonomous system in the vicinity of a compound critical point is studied in detail. The critical point is characterized by two distinct pairs of pure imaginary eigenvalues of the Jacobian, and the system is described by two independent parameters. The analysis is based on a generalized perturbation procedure which employs mul...

3D free boundary equilibrium computations have recently been used to model external kinks and edge harmonic oscillations (EHOs), comparing with linear MHD stability codes, nonlinear analytic theory [Kleiner et al., Phys. Plasma Controlled Fusion 61, 084005 (2019)]. In this study, results of the VMEC code are compared further reduced simulations, using JOREK code. The purpose investigation was u...

— We prove stability of the bound states for the quantum harmonic oscillator under non-resonant, time quasi-periodic perturbations by proving that the associated Floquet Hamiltonian has pure point spectrum. Résumé (Stabilité de l’oscillateur harmonique quantique sous les perturbations quasipériodiques) Nous démontrons la stabilité des états bornés de l’oscillateur harmonique sous les perturbati...

Based on a recent study of the linearized Bianchi equations by Buchman and Sarbach, we construct and implement a hierarchy of absorbing boundary conditions for the Einstein equations in generalized harmonic gauge. As a test problem, we demonstrate that we can evolve multipolar gravitational waves without any spurious reflections at linear order in perturbation theory.

Lattice networks of oscillators have been considered for a long time as good models for studying macroscopic energy trasport and its diffusion, i.e. for obtaining, on a macroscopic space-time scale, heat equation and Fourier law of conduction ([1]). It is well understood that the diffusive behavior of the energy is due to the non-linearity of the interactions, and that purely deterministic harm...

We show that quantum mechanics admits a local analytic formulation. This formulation shows that the perturbation series arising in quantum integrable systems are resummable, possibly after a rescaling of the deformation parameter with respect to the Planck constant. In particular, the spectrum of the perturbed harmonic oscillator is resummable.

We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.