Related Experiment Video
Updated: Jan 6, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
8.9K
Balancing long-range interactions and quantum pressure: Solitons in the Hamiltonian mean-field model
Ryan Plestid1,2, D H J O'Dell1
1Department of Physics and Astronomy, McMaster University, 1280 Main St. W., Hamilton, Ontario, Canada L8S 4M1.
Physical Review. E
|October 3, 2019
Summary
Researchers explored the quantum Hamiltonian mean-field (HMF) model, finding novel bright solitons supported by long-range interactions. These solitary waves exhibit unique properties distinct from short-range interaction models.
Area of Science:
- Statistical Mechanics
- Quantum Mechanics
- Nonlinear Physics
Background:
- The Hamiltonian mean-field (HMF) model is a generic statistical mechanical system for long-range interactions.
- It captures universal effects of long-range forces, like gravity, and is exactly solvable.
- Recent experiments use the HMF model for cold atoms with optically mediated interactions.
Purpose of the Study:
- To classify stationary solutions of the quantum HMF model in one dimension.
- To analyze the generalized Gross-Pitaevskii equation (GGPE) for the quantum HMF model.
- To understand the unique behavior of solitary waves in systems with long-range interactions.
Main Methods:
- Consideration of the quantum version of the HMF model.
- Analysis of the nonlinear and nonlocal generalized Gross-Pitaevskii equation (GGPE).
- Identification of exact solutions as Mathieu functions.
Main Results:
- Stationary solutions of the quantum HMF model's GGPE were classified.
- Exact solutions were identified as bright solitons (Mathieu functions).
- A novel 'tower of solitons' with varying nodes was discovered, unlike short-range models.
Conclusions:
- Long-range interactions in the HMF model support solitary waves in a unique way.
- The study provides insights into nonlinear phenomena driven by long-range forces.
- Results suggest novel solitary wave dynamics in quantum systems with non-local interactions.
Related Concept Videos
02:45The Quantum-Mechanical Model of an Atom
56.4K
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.
56.4K
01:23Equilibrium Conditions for a Particle
2.1K
When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
2.1K
01:10First Law: Particles in One-dimensional Equilibrium
7.9K
Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...
7.9K
01:24Van der Waals Interactions
69.9K
Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions between particles with permanent, partial, or temporary charges. The intermolecular forces between neutral atoms and molecules are ion–dipole, dipole–dipole, and dispersion forces, collectively known as van der Waals forces.
69.9K
01:13Basic Equation for Pressure Field
527
The basic equation for a pressure field in fluid mechanics captures the balance of forces within any segment of fluid, providing a foundational understanding of how pressure changes within fluids under various forces. Generally, two main types of forces act on any part of a fluid: surface forces and body forces. Surface forces arise from pressure differences across points within the fluid, which result in net forces that can vary depending on the local pressure gradient. Body forces, on the...
527
01:18First Law: Particles in Two-dimensional Equilibrium
13.9K
Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about...
Newton's first law tells us about...
13.9K