Related Experiment Video
Updated: Jul 17, 2026
09:23
Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
Nonlinear quantum shock waves in fractional quantum Hall edge states
E Bettelheim1, Alexander G Abanov, P Wiegmann
1James Frank Institute, University of Chicago, 5640 S. Ellis Avenue, Chicago, Illinois 60637, USA.
Physical Review Letters
|February 7, 2007
Summary
Transport in electronic systems is nonlinear and unstable, leading to shock waves and localized pulses with fractional charges. This research explores quantum shock waves and fractional charge measurements in fractional quantum Hall edge states.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
Background:
- Interacting nondissipative electronic systems exhibit complex transport phenomena.
- The Calogero model provides a framework for studying such systems, particularly edge states.
Purpose of the Study:
- To demonstrate the nonlinear and unstable nature of transport in interacting nondissipative electronic systems using the Calogero model.
- To investigate the formation of shock waves and fractionally quantized charge pulses.
- To explore the potential for observing quantum shock waves and measuring fractional charge in fractional quantum Hall edge states.
Main Methods:
- Utilizing the Calogero model to analyze electronic transport.
- Investigating nonlinear effects arising from the electronic spectrum's curvature near the Fermi energy.
- Analyzing the evolution of semiclassical wave packets.
Main Results:
- Transport in these systems is fundamentally nonlinear and unstable.
- Propagating wave packets develop shock waves and collapse into localized, fractionally charged pulses.
- The Calogero model effectively describes fractional quantum Hall edge states.
Conclusions:
- Nonlinear dynamics govern transport in interacting nondissipative electronic systems.
- Quantum shock waves and fractional charge are key emergent phenomena.
- Experimental observation of these phenomena in fractional quantum Hall edge states is feasible.
Related Concept Videos
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...
01:28Standing 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:
01:16Shock Waves
While deriving the Doppler formula for the observed frequency of a sound wave, it is assumed that the speed of sound in the medium is greater than the source's speed through it. When this condition is breached, a shock wave occurs.
When the source's speed approaches the speed of sound, constructive interference between successive wavefronts emitted by the source occurs immediately behind it. Initially, scientists believed that this constructive interference would result in such high pressures...
When the source's speed approaches the speed of sound, constructive interference between successive wavefronts emitted by the source occurs immediately behind it. Initially, scientists believed that this constructive interference would result in such high pressures...
01:30The Hall Effect
Edwin H. Hall, in the year 1879, devised an experiment that could be used to identify the polarity of the predominant charge carriers in a conducting material. From a historical perspective, this experiment was the first to demonstrate that the charge carriers in most metals are negative.
02:45The Quantum-Mechanical Model of an Atom
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
01:02¹H NMR: Interpreting Distorted and Overlapping Signals
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...