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Forced Oscillations

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When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.

Damped Oscillations

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In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
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One-Degree-of-Freedom System

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If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...

Second Order systems II

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Related Experiment Video

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Numerical study on dynamical behavior in oscillatory driven quantum double-well systems.

Akira Igarashi¹, Hiroaki Yamada

¹Graduate School of Science and Technology, Niigata University, Ikarashi 2-Nochou 8050, Niigata 950-2181, Japan. igara4.akira@gs.niigata-u.ac.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 15, 2008

Summary

Quantum dynamics in a double-well system exhibit coherent or incoherent motion based on polychromatic perturbation. Increasing perturbation strength or frequencies drives a transition from coherent tunneling to decoherence-induced delocalization.

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Area of Science:

Quantum mechanics
Nonlinear dynamics
Condensed matter physics

Background:

Quantum systems in double-well potentials are fundamental for studying tunneling and coherence.
Parametric perturbations can significantly alter quantum dynamics, leading to phenomena like chaos and decoherence.

Purpose of the Study:

To numerically investigate the influence of polychromatic perturbations on quantum dynamics in a 1D double-well system.
To differentiate between coherent and incoherent quantum motion based on perturbation parameters and analyze their characteristics.

Main Methods:

Numerical simulations of a one-dimensional double-well system.
Analysis of transition probabilities, expectation values, standard deviations, and Wigner function negativity.
Comparison of quantum dynamics classification with classical dynamics using Lyapunov exponents.

Main Results:

Identified two distinct types of motion: coherent and incoherent, dependent on perturbation parameters.
Observed a transition from coherent tunneling to decoherence-induced delocalization with increased perturbation strength or frequency components.
Found that Wigner function negativity mirrors the time dependence of quantum dynamics in both motion types.
Demonstrated a strong overlap between quantum and classical dynamics classifications in the parameter space.
Confirmed decoherence in a kicked double-well system.

Conclusions:

Polychromatic parametric perturbations can induce distinct coherent and incoherent quantum dynamics in double-well systems.
The transition from coherent to incoherent motion is linked to the loss of quantum coherence due to the perturbation.
Classical and quantum dynamics classifications show remarkable agreement, suggesting shared underlying mechanisms.
The study provides insights into controlling and understanding quantum dynamics in complex perturbed systems.