On the Breakdown of Perturbation Theory †
نویسنده
چکیده
The production of o(1 g 2) particles in a weakly-coupled theory is believed to be non-perturbatively suppressed. I comment on the prospects of (a) establishing this rigorously, and (b) estimating the effect to exponential accuracy semiclassically, by discussing two closely-related problems: the large-order behaviour of few-point Green functions, and induced excitation in quantum mechanics. Induced tunneling in the latter case is exponentially enhanced for frequencies of the order of the barrier height.
منابع مشابه
Nonlinear analysis of radially functionally graded hyperelastic cylindrical shells with axially-varying thickness and non-uniform pressure loads based on perturbation theory
In this study, nonlinear analysis for thick cylindrical pressure vessels with arbitrary variable thickness made of hyperelastic functionally graded material properties in nearly incompressible state and clamped boundary conditions under non-uniform pressure loading is presented. Thickness and pressure of the shell are considered in axial direction by arbitrary nonlinear profiles. The FG materia...
متن کاملAnalytic Equation of State for the Square-well Plus Sutherland Fluid from Perturbation Theory
Analytic expressions were derived for the compressibility factor and residual internal energy of the square-well plus Sutherland fluid. In this derivation, we used the second order Barker-Henderson perturbation theory based on the macroscopic compressibility approximation together with an analytical expression for radial distribution function of the reference hard sphere fluid. These properties...
متن کاملEffects of Stress Grading Materials’ Properties on the Performance of 20-kV Cable Terminations
Stress grading (SG) layer in cable terminations limits the critical electric field and properties of SG materials are important issues which have to be considered during manufacturing and selecting procedure. In this paper, two different types of (SG) materials are analyzed by both theory and test. According to the applied theory, important parameters as: electrical resistivity, breakdown volta...
متن کاملDynamic response determination of viscoelastic annular plates using FSDT – perturbation approach
In this paper, the transient response of a viscoelastic annular plate which has time-dependent properties is determined mathematically under dynamic transverse load. The axisymmetric conditions are considered in the problem. The viscoelastic properties obey the standard linear solid model in shear and the bulk behavior in elastic. The equations of motion are extracted using Hamilton’s principle...
متن کاملSingular Perturbation Theory in Output Feedback Control of Pure-Feedback Systems
This paper studies output feedback control of pure-feedback systems with immeasurable states and completely non-affine property. Since availability of all the states is usually impossible in the actual process, we assume that just the system output is measurable and the system states are not available. First, to estimate the immeasurable states a state observer is designed. Relatively fewer res...
متن کاملA study on the use of perturbation technique for analyzing the nonlinear forced response of piezoelectric microcantilevers
In this paper, a comparison is made between direct and indirect perturbation approaches to solve the non-linear vibration equations of a piezoelectrically actuated cantilever microbeam. In this comparison, the equation of motion is considered according to Euler-Bernoulli theory with considering the non-linear geometric and inertia terms resulted from shortening effect. In the direct perturbatio...
متن کامل