Related Experiment Video
Updated: Aug 2, 2025
08:03
Study of Protein Dynamics via Neutron Spin Echo Spectroscopy
Published on: April 13, 2022
2.2K
Dynamical chaos in nonlinear Schrödinger models with subquadratic power nonlinearity
Alexander V Milovanov1,2, Alexander Iomin2,3
1ENEA National Laboratory, Centro Ricerche Frascati, 00044 Frascati, Rome, Italy.
Physical Review. E
|April 19, 2023
Summary
This study introduces a new analytical method for nonlinear Schrödinger lattices, revealing subdiffusive spreading with Lévy flights due to system degeneracies. The findings detail complex field organization and localization phenomena.
Area of Science:
- Nonlinear dynamics
- Condensed matter physics
- Mathematical physics
Background:
- Nonlinear Schrödinger lattices are crucial for modeling wave phenomena.
- Understanding field spreading in disordered systems is a key challenge.
- Perturbation theory often fails for strong nonlinearities and disorder.
Purpose of the Study:
- To develop an analytical method for nonlinear Schrödinger lattices with random potentials and subquadratic nonlinearity.
- To investigate the asymptotic spreading dynamics of the nonlinear field.
- To analyze the role of system degeneracies and nonlinearity orders.
Main Methods:
- Development of an iteration algorithm based on the multinomial theorem.
- Utilizing Diophantine equations and mapping onto a Cayley graph.
- Analytical derivation of results beyond perturbation theory.
Main Results:
- Demonstration of subdiffusive spreading of the nonlinear field.
- Identification of complex microscopic organization, including trapping and Lévy flights.
- Association of Lévy flights with degenerate states characteristic of subquadratic nonlinearity.
- Analysis of the transition from Anderson localization to stochastic delocalization at the quadratic nonlinearity limit.
Conclusions:
- The developed analytical method provides new insights into complex spreading phenomena in disordered nonlinear systems.
- Degenerate states play a critical role in the observed subdiffusive transport and Lévy flight behavior.
- The study elucidates the impact of nonlinearity order on field localization and delocalization.
More Related Videos
Related Concept Videos
01:21Linear Approximation in Time Domain
110
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
110
02:45The Quantum-Mechanical Model of an Atom
42.6K
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.
42.6K
01:10Entropy Change in Reversible Processes
2.6K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
2.6K
01:26Linear Approximation in Frequency Domain
120
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
120
01:22Nonlinear Pharmacokinetics: Causes of Nonlinearity
272
Nonlinearity in drug pharmacokinetics is caused by various factors influencing how a drug is absorbed, distributed, metabolized, and excreted. Understanding these nonlinear processes is crucial for predicting drug behavior in the body and optimizing drug dosing regimens.
Nonlinear drug absorption can occur when the process is rate-limited by solubility, carrier-mediated transport systems, or saturation of the presystemic gut wall or hepatic metabolism. For instance, high doses of riboflavin...
Nonlinear drug absorption can occur when the process is rate-limited by solubility, carrier-mediated transport systems, or saturation of the presystemic gut wall or hepatic metabolism. For instance, high doses of riboflavin...
272
01:13Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model
100
Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
100