Related Experiment Video
Updated: Jul 8, 2026
08:04
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
Generalized Gross-Pitaevskii Equation for 2D Bosons with Attractive Interactions
Michał Suchorowski1, Fabian Brauneis2, Hans-Werner Hammer2,3
1University of Warsaw, Faculty of Physics, Pasteura 5, 02-093 Warsaw, Poland.
Physical Review Letters
|July 7, 2026
Summary
We present a new theory for 2D attractive Bose systems using a generalized Gross-Pitaevskii equation. This model captures quantum anomalies and predicts novel quantum droplets and excited states, aiding experimental research.
Area of Science:
- Quantum physics
- Condensed matter theory
- Bose-Einstein condensates
Background:
- Standard mean-field equations lack scale invariance.
- Studying 2D attractive Bose systems requires advanced theoretical frameworks.
Purpose of the Study:
- Introduce a generalized Gross-Pitaevskii equation for 2D attractive Bose systems.
- Incorporate quantum anomaly effects via logarithmic density dependence.
- Explore static and dynamic properties of finite Bose systems.
Main Methods:
- Developed a nonlinear framework based on a generalized Gross-Pitaevskii equation.
- Analyzed universal bound states (quantum droplets) in free space.
- Investigated breathing modes and quench dynamics in trapped systems.
Main Results:
- The new framework breaks scale invariance, enabling quantum anomaly calculations.
- Predicted universal excited states, including vortex configurations.
- Established a foundation for studying static and dynamic properties.
Conclusions:
- The generalized equation offers a robust theoretical basis for 2D attractive Bose systems.
- Results guide future experimental investigations of quantum droplets and nonequilibrium phenomena.
- Predicted states may be more experimentally accessible than ground states.
Related Concept Videos
01:10Van der Waals Equation
The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
01:27Lattice Energies of Ionic Crystals
Lattice energy represents the energy released when gaseous cations and anions combine to form an ionic solid, reflecting the strength of electrostatic interactions within the crystal. This process is fundamentally governed by Coulombic attraction between oppositely charged ions, where the potential energy varies inversely with the interionic distance and directly with the product of ionic charges. As ions approach one another, the electrostatic energy becomes increasingly negative, indicating a...
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.
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.
03:06The Pauli Exclusion Principle
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
01:18First Law: Particles in Two-dimensional Equilibrium
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 the...
Newton's first law tells us about the...