Related Experiment Video
Updated: Jan 30, 2026
05:52
In Situ Measurement and Correlation of Cell Density and Light Emission of Bioluminescent Bacteria
Published on: June 28, 2018
12.2K
Wigner high-electron-correlation regime of nonuniform density systems: A quantal-density-functional-theory study
Douglas Achan1, Lou Massa1, Viraht Sahni1
1The Graduate School of the City University of New York, 365 Fifth Avenue, New York, NY 10016.
Physical Review. A, Atomic, Molecular, and Optical Physics
|January 12, 2019
Summary
The Wigner regime is characterized by high correlation-kinetic energy, unlike the low correlation regime. Quantal density functional theory (QDFT) reveals
Area of Science:
- Quantum mechanics
- Computational chemistry
- Condensed matter physics
Background:
- The Wigner regime signifies low electron density and high interaction energy relative to kinetic energy.
- The low correlation regime is defined by high electron density and lower interaction energy than kinetic energy.
Purpose of the Study:
- Investigate the Wigner regime of nonuniform electron density systems using quantal density functional theory (QDFT).
- Delineate contributions of electron correlations (Pauli, Coulomb, correlation-kinetic) within QDFT.
- Obtain exact values for Kohn-Sham exchange-correlation and correlation energy functionals.
Main Methods:
- Utilized quantal density functional theory (QDFT) for analysis.
- Studied Hooke's atom in the Wigner regime to derive exact wave functions.
- Analyzed energy components including Hartree, Pauli, Coulomb, and correlation-kinetic energies.
Main Results:
- In the Wigner regime, electron-interaction energy and its components (Hartree, Pauli, Coulomb) are greater fractions of total energy compared to the low correlation case.
- The ionization potential as a fraction of total energy is also greater in the Wigner regime.
- Correlation-kinetic energy is substantially higher in the Wigner regime, leading to a proposed characterization by high correlation-kinetic energy.
Conclusions:
- The Wigner regime is characterized by high correlation-kinetic energy, contrasting with the low correlation regime.
- Introduced 'quantal compression' and 'quantal decompression' concepts to explain kinetic energy density behavior.
- Provided exact values for Kohn-Sham functionals, valuable for developing new approximate functionals for the Wigner regime.
Related Concept Videos
00:56Density
19.9K
Density is an important characteristic of substances, crucial in determining whether an object sinks or floats in a fluid. Its SI unit is kg/m3, and its cgs unit is g/cm3. The density of an object helps in identifying its composition, and also reveals information about the phase of the matter and its substructure. The densities of liquids and solids are roughly comparable, consistent with the fact that their atoms are in close contact. However, gases have much lower densities than liquids and...
19.9K
01:27Applications of Integration to Probability Density Functions
54
Continuous probability distributions are used to model random variables that can take on any real value within a specified range. These variables do not take on isolated or countable values but rather exist on a continuum. For example, the height of an individual can be measured with increasing precision—such as 163.5 or 165.25 centimeters—demonstrating that height is a continuous random variable.The behavior of such variables is described using a probability density function (PDF),...
54
01:21Current Density
5.1K
The total amount of current flowing through one unit value of a cross-sectional area is referred to as current density. If the current flow is uniform, the amount of current flowing through a conductor is the same at all points along the conductor, even if the conductor area varies. The current density consists of the local magnitude and direction of the charge flow, which varies from point to point. Current density is measured in amperes per meter square, and direction is defined as the net...
5.1K
01:20Strain-Energy Density
907
Understanding the strain energy density in materials under axial load is crucial for evaluating their mechanical behavior and durability. When a rod is subjected to such a load, it elongates and stores energy, known as strain energy, as potential energy within the material. This energy is measured in terms of energy per unit volume.
In the elastic region of a material, the relationship between the stress and the strain is linear and follows Hooke's Law. The strain energy density in this region...
In the elastic region of a material, the relationship between the stress and the strain is linear and follows Hooke's Law. The strain energy density in this region...
907
01:22Bulk Density of Aggregate
1.2K
Bulk density refers to the mass of aggregate particles that would fill a unit volume. The concept of bulk density originates from the inability to pack aggregate particles in a manner that completely eliminates void spaces. Hence, the term bulk refers to the volume that encompasses both the aggregates and the voids. This measurement is crucial when aggregates are batched by volume and is used to convert quantities by mass to volume.
Most natural mineral aggregates, like sand and gravel,...
Most natural mineral aggregates, like sand and gravel,...
1.2K
01:05Density and Archimedes' Principle
8.9K
When a lump of clay is dropped into water, it sinks. But if the same lump of clay is molded into the shape of a boat, it starts to float. Because of its shape, the clay boat displaces more water than the lump and experiences a greater buoyant force, even though its mass is the same. The same holds true for steel ships. The average density of an object majorly determines if the object will float. If an object's average density is less than that of the surrounding fluid, it will float. The...
8.9K