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Damped Oscillations

Damped Oscillations

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.
Although friction and other non-conservative...

Types of Damping

Types of Damping

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...

Forced Oscillations

Forced Oscillations

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.

RLC Series Circuits

RLC Series Circuits

An RLC series circuit comprises an inductor, a resistor, and a charged capacitor connected in series. When the circuit is closed, the capacitor begins to discharge through the resistor and inductor by transferring energy from the electric field to the magnetic field. Here, the resistor connected to the circuit causes energy losses; therefore, on the complete discharge of the capacitor, the magnetic field energy acquired by the inductor is less than the original electric field energy of the...

Magnetic Damping

Magnetic Damping

Eddy currents can produce significant drag on motion, called magnetic damping. For instance, when a metallic pendulum bob swings between the poles of a strong magnet, significant drag acts on the bob as it enters and leaves the field, quickly damping the motion.
If, however, the bob is a slotted metal plate, the magnet produces a much smaller effect. When a slotted metal plate enters the field, an emf is induced by the change in flux; however, it is less effective because the slots limit the...

RLC Circuit as a Damped Oscillator

RLC Circuit as a Damped Oscillator

An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
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...

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Related Experiment Video

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Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

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Published on: March 30, 2017

Low-temperature quantum fluctuations in overdamped ratchets.

Stefan A Maier¹, Joachim Ankerhold

¹Institut für Theoretische Physik, Universität Ulm, Germany.

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

|September 28, 2010

Summary

Quantum fluctuations impact directed transport in ratchets at low temperatures. Higher-order corrections can alter or even reverse current flow, offering insights into quantum Smoluchowski equation dynamics.

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Area of Science:

Quantum physics
Statistical mechanics

Background:

The time evolution of density distribution in position at low temperatures and strong friction follows a quantum Smoluchowski equation.
Higher-order contributions of quantum fluctuations to drift and diffusion coefficients have been systematically derived.

Purpose of the Study:

To investigate directed transport in ratchets as a complex system to reveal the impact of subleading quantum corrections.
To demonstrate the convergence properties of the perturbation series in quantum transport.

Main Methods:

Analysis of directed transport in ratchets under specific low-temperature and high-friction conditions.
Systematic derivation and application of higher-order quantum fluctuation corrections to drift and diffusion coefficients.
Examination of perturbation series behavior and its dependence on system symmetry properties.

Main Results:

The perturbation series for quantum transport in ratchets typically exhibits non-monotonous behavior.
Higher-order quantum corrections can significantly influence directed transport, potentially compensating for current reversals induced by leading quantum fluctuations.
The study reveals the complex interplay between quantum fluctuations and system symmetry in determining transport direction.

Conclusions:

Consistent treatment of overdamped quantum systems at low temperatures is crucial for accurate numerical applications.
Subleading quantum corrections play a vital role in understanding quantum transport phenomena.
The findings provide a framework for analyzing quantum dynamics in systems like ratchets, particularly concerning the convergence of theoretical models.