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Related Concept Videos

Damped Oscillations01:07

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...
Forced Oscillations01:06

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.
The de Broglie Wavelength02:32

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
Types of Damping01:20

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...
Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
Design Example: Underdamped Parallel RLC Circuit01:17

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Consider designing an oscillator circuit, a crucial component in various electronic devices and systems. The objective is to create an oscillator circuit with specific characteristics: a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. To accomplish this, a parallel RLC circuit is employed, known for its ability to sustain oscillations at a resonant frequency. In this case, the damping factor is pivotal in achieving the desired performance.
Starting with a fixed...

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Dynamic quantum tunneling in mesoscopic driven Duffing oscillators.

Lingzhen Guo1, Zhigang Zheng, Xin-Qi Li

  • 1Department of Physics, Beijing Normal University, 100875 Beijing, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 27, 2011
PubMed
Summary
This summary is machine-generated.

We studied quantum tunneling in a mesoscopic driven Duffing oscillator. Mesoscopic effects create a linear relationship between tunneling rates and the distance from the shifted bifurcation point.

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Area of Science:

  • Quantum physics
  • Nonlinear dynamics
  • Mesoscopic systems

Background:

  • The Duffing oscillator is a fundamental model in nonlinear dynamics.
  • Quantum tunneling is a phenomenon where particles pass through energy barriers.
  • Mesoscopic systems bridge the gap between quantum and classical physics.

Purpose of the Study:

  • To investigate dynamic quantum tunneling in a mesoscopic driven Duffing oscillator.
  • To understand the influence of mesoscopic effects on tunneling dynamics.
  • To explore the relationship between tunneling rate and bifurcation points.

Main Methods:

  • Theoretical analysis of a driven Duffing oscillator model.
  • Focus on mesoscopic system properties.
  • Examination of quantum tunneling dynamics.

Main Results:

  • Observed a significant quantum shift in the bifurcation point.
  • Discovered a perfect linear scaling of tunneling rate with driving distance to the shifted bifurcation point.
  • Demonstrated the impact of mesoscopic nature on tunneling behavior.

Conclusions:

  • Mesoscopic effects notably alter quantum tunneling dynamics in driven Duffing oscillators.
  • The identified linear scaling provides a new quantitative understanding of tunneling near bifurcation points.
  • This research offers insights into quantum phenomena in macroscopic systems.