Anharmonic oscillator: a playground to get insight into renormalization

  title={Anharmonic oscillator: a playground to get insight into renormalization},
  author={Saman Moghimi-Araghi and Farhang Loran},
  journal={European Journal of Physics},
In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used in quantum field theory (QFT) where the bare values of the parameters of the theory run when an interaction is added. In this paper, we review some of these techniques and introduce some new ones in line with QFT methods. Moreover, we investigate the case of… 
1 Citations

Non-linear resonance in the simplest RLC circuit

We describe an undergraduate experiment demonstrating a non-linear oscillator based on a simple RLC circuit. Non-linearity is introduced by a single, reverse biased, diode. The response curves are



Application of Hamilton's principle to the study of the anharmonic oscillator in classical mechanics

A form of Hamilton’s principle for classical mechanics, appropriate to the study of arbitrary self‐sustained vibrations in one dimension is presented. It is applied as an approximate computational

Quantum Electrodynamics

THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To

Harmonic and anharmonic behaviour of a simple oscillator

We consider a simple oscillator that exhibits harmonic and anharmonic regimes and analyse its behaviour over the complete range of possible amplitudes. The oscillator consists of a mass m fixed at

Nonlinear dynamics: A tutorial on the method of normal forms

We consider a variety of nonlinear systems, described by linear differential equations, subjected to small nonlinear perturbations. Approximate solutions are sought in terms of expansions in a small

A new perturbative approach to nonlinear problems

A recently proposed perturbative technique for quantum field theory consists of replacing nonlinear terms in the Lagrangian such as φ4 by (φ2)1+δ and then treating δ as a small parameter. It is shown

Comment on ‘Improving series convergence: the simple pendulum and beyond’

In this comment we analyze the improved series proposed by Duki et al (2018 Eur. J. Phys. 39 065802) for the approximate calculation of a variety of physical quantities like the period of the simple

Finite-Temperature Field Theory: Principles and Applications

1. Review of quantum statistical mechanics 2. Functional integral representation of the partition function 3. Interactions and diagrammatic techniques 4. Renormalisation 5. Quantum electrodynamics 6.

The Duffing Equation: Nonlinear Oscillators and their Behaviour

List of Contributors. Preface. 1 Background: On Georg Duffing and the Duffing Equation (Ivana Kovacic and Michael J. Brennan). 1.1 Introduction. 1.2 Historical perspective. 1.3 A brief biography of

Introduction to the method of multiple scales

Earlier versions of these lecture notes have been used at the Cork Summerschool on Theory and Mathematics Modelling of Ultrashort Pulse Propagation (2013), and as a part of a graduate course in the