Related Experiment Video
Updated: Jul 10, 2025

Microwave Photonics Systems Based on Whispering-gallery-mode Resonators
Published on: August 5, 2013
Geometric phase for nonlinear oscillators from perturbative renormalization group
D A Khromov1, M S Kryvoruchko2, D A Pesin3
1Moscow Institute of Physics and Technology, Dolgoprudny, 141701 Moscow Region, Russia.
Abstract:
We formulate a renormalization-group approach to a general nonlinear oscillator problem. The approach is based on the exact group law obeyed by solutions of the corresponding ordinary differential equation. We consider both the autonomous models with time-independent parameters, as well as nonautonomous models with slowly varying parameters. We show that the renormalization-group equations for the nonautonomous case can be used to determine the geometric phase acquired by the oscillator during the change of its parameters. We illustrate the obtained results by applying them to the Van der Pol and Van der Pol-Duffing models.
Related Concept Videos
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
Oscillations about an Equilibrium Position
Damped Oscillations
Although friction and other non-conservative...
Second Order systems II
RLC Circuit as a Damped Oscillator
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...

