Related Experiment Video
Updated: Jul 2, 2026
15:06
Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle
Published on: January 3, 2016
Nonlinear Schrödinger equation with random Gaussian input: distribution of inverse scattering data and eigenvalues.
Pavlos Kazakopoulos1, Aris L Moustakas
1Department of Physics, University of Athens, Athens 15784, Greece.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 4, 2008
Summary
We calculated the Lyapunov exponent and density of states for nonlinear Schrödinger equations with random pulses. This research has implications for information transmission in optical fibers.
Area of Science:
- Nonlinear dynamics
- Quantum mechanics
- Optical physics
Background:
- The nonlinear Schrödinger equation (NLSE) models various physical phenomena, including wave propagation in optical fibers.
- Non-Hermitian operators and random potentials introduce complexities in spectral analysis.
- Understanding spectral properties is crucial for predicting system behavior and stability.
Purpose of the Study:
- To calculate the Lyapunov exponent for the non-Hermitian Zakharov-Shabat eigenvalue problem.
- To determine the average density of states for the attractive nonlinear Schrödinger equation with random initial conditions.
- To analyze the distribution of scattering data and its impact on eigenfunction asymptotics.
Main Methods:
- Extension of the Thouless formula to non-Hermitian random operators.
- Calculation of Lyapunov exponents and average density of states.
- Analysis of scattering data distribution for complex and real Gaussian random pulses.
Main Results:
- The Lyapunov exponent and average density of states were successfully calculated for the specified non-Hermitian eigenvalue problem.
- The distribution of scattering data was determined, providing insights into eigenfunction behavior.
- Two distinct cases involving circularly symmetric complex and real Gaussian pulses were analyzed.
Conclusions:
- The study provides a theoretical framework for analyzing spectral properties of NLSE with random potentials.
- The findings offer insights into signal stability and transmission characteristics in nonlinear optical systems.
- This research contributes to understanding information transmission limits in nonlinear optical fibers.
More Related Videos
06:49In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation
Published on: March 2, 2021
11:34Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels
Published on: September 8, 2016
Related Concept Videos
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...
01:25Poisson's And Laplace's Equation
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
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...
01:20Maxwell-Boltzmann Distribution: Problem Solving
Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
01:07Gauss's Law
If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
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...