Related Experiment Video
Updated: Jul 2, 2026
05:39
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
Tunneling mediated by 2D+1 conical waves in a 1D lattice
Andrea Di Falco1, Claudio Conti, Stefano Trillo
1School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews, KY16 9SS, United Kingdom.
Physical Review Letters
|September 4, 2008
Summary
Nonlinear wave packets in 1D band gap systems spontaneously form localized waves. This nonlinear tunneling exhibits distinct edge behaviors, driven by competing bullets and nonlinear X waves.
Area of Science:
- Nonlinear optics
- Condensed matter physics
- Wave propagation
Background:
- Band gap systems exhibit unique wave propagation properties.
- Nonlinearity can significantly alter wave dynamics.
- Understanding wave packet behavior is crucial in various physical systems.
Purpose of the Study:
- To investigate the propagation of 2D+1 wave packets in 1D band gap systems.
- To analyze the role of periodicity and nonlinearity in wave localization.
- To characterize the formation and dynamics of localized waves.
Main Methods:
- Numerical simulations of wave packet propagation.
- Analysis of wave packet dynamics in the presence of nonlinearity.
- Examination of system behavior at band gap edges.
Main Results:
- Spontaneous formation of fast and slow conical localized waves.
- Observation of distinct nonlinear tunneling features on different band gap edges.
- Identification of competition between 'bullets' and nonlinear X waves.
Conclusions:
- Periodicity and nonlinearity interplay to create novel localized wave structures.
- Nonlinear tunneling in band gap systems is complex and asymmetric.
- The dynamics are governed by a competition between different wave types.
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:
01:12Bewley Lattice Diagram
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
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...
02:33Lattice Centering and Coordination Number
The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
Types of Unit Cells
Imagine taking a large number of identical...
02:54Trends in Lattice Energy: Ion Size and Charge
An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
01:27Traveling Waves: Lossless Lines
The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx and a shunt capacitance CΔx.