Related Experiment Video
Updated: Jun 14, 2026
11:45
Experimental Methods for Trapping Ions Using Microfabricated Surface Ion Traps
Published on: August 17, 2017
Friedel oscillations in microwave billiards
A Bäcker1, B Dietz, T Friedrich
1Institut für Theoretische Physik, Technische Universität Dresden, Dresden, Germany.
Summary
Researchers found that a random plane-wave model accurately describes electron density oscillations in pseudointegrable microwave billiards. This model also applies to mixed systems when accounting for chaotic and regular states using phase-space projection.
Area of Science:
- Quantum mechanics
- Wave phenomena
- Classical chaos
Background:
- Friedel oscillations describe electron density variations near step edges in materials.
- Microwave billiards serve as a physical model for studying wave phenomena in complex geometries.
- Random plane-wave models are typically used for chaotic systems.
Purpose of the Study:
- To investigate the applicability of a random plane-wave model to non-purely-chaotic dynamical systems.
- To explore analogies between electron density oscillations and wave patterns in microwave billiards.
- To test the model's performance on pseudointegrable and mixed dynamics geometries.
Main Methods:
- Experimental measurements in microwave cavities with pseudointegrable and mixed dynamics geometries.
- Application and testing of a random plane-wave model.
- Development of phase-space projection techniques for mixed systems.
Main Results:
- The random plane-wave model successfully described oscillations in the pseudointegrable microwave cavity.
- The model's agreement with experimental data for mixed systems improved significantly after incorporating phase-space projection.
- The study demonstrated the utility of microwave billiards as an analog for studying quantum phenomena.
Conclusions:
- A random plane-wave model can effectively describe wave phenomena in systems beyond purely chaotic ones.
- Phase-space projection is crucial for accurately modeling mixed dynamics in such systems.
- The findings offer insights into wave behavior in complex and partially regular systems.
Related Concept Videos
01:28Standing Waves in a Cavity
A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
02:18Interference and Diffraction
Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
02:32The 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...
01:30Oscillations In An LC Circuit
An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by
01:04Oscillations about an Equilibrium Position
Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so because...
01:23Atomic Nuclei: Nuclear Relaxation Processes
In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis, the precessing magnetic moments are randomly oriented around the z-axis. This...