Related Experiment Video
Updated: Jul 11, 2026
05:51
Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method
Published on: July 19, 2019
Improved quantum hard-sphere ground-state equations of state
M A Solís1, M de Llano, J W Clark
1Department of Physics, Washington University, St. Louis, Missouri 63130, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
Summary
This study presents an improved energy formula for boson and fermion hard-sphere systems. The new formula accurately predicts ground-state energy across various densities, aligning well with simulation data.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Condensed matter physics
Background:
- The London energy formula describes ground-state energy for boson hard spheres.
- Generalizing this to fermion systems and improving fluid branches is crucial for understanding dense quantum matter.
Purpose of the Study:
- To develop an improved ground-state energy formula for boson and fermion hard-sphere systems.
- To accurately model systems across a range of densities, from low to close-packing.
Main Methods:
- Generalized the London formula for bosons to include fermions with multiple degrees of freedom.
- Constructed improved fluid branches using perturbation theory and Padé approximants.
- Extrapolated low-density expansions to intermediate and high densities.
Main Results:
- The generalized formula exhibits a double-pole at close-packing density for crystalline phases.
- Improved fluid branches accurately model irregular or random close-packing.
- Results show excellent agreement with Green-function Monte Carlo, diffusion Monte Carlo, and other advanced simulation methods.
Conclusions:
- The developed formula offers a more accurate description of ground-state energy for hard-sphere quantum systems.
- This work provides a robust theoretical tool for studying dense boson and fermion systems.
Related Concept Videos
01:07Equation of State
The equation of state is an equation that relates physical quantities, such as pressure, volume, temperature, and the number of moles, of a thermodynamics system with each other. The equation relating physical quantities with each other can be a simple mathematical expression or too complicated to express in mathematical form. In either case, a relationship between physical quantities exists. If the equation of state cannot be expressed in a mathematical form, then experimental data and...
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...
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...
01:23Equilibrium Conditions for a Particle
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...
01:26The Van der Waals Equation
The ideal gas law is based on two simplifying assumptions: first, that there are no intermolecular attractions between gas molecules, and second, that the volume occupied by the molecules themselves is negligible compared with the volume of the container. However, these assumptions don't hold up under all conditions - specifically, at high pressures and low temperatures, as gas tends to deviate from ideal gas behavior.The van der Waals equation is an enhanced version of the ideal gas law,...
01:27Variables and Equations of State
The physical state of a pure substance can be defined by certain state variables such as volume (V), pressure (p), temperature (T), and amount of substance (n). When two gases are separated by a movable wall, the gas with the higher pressure naturally compresses the gas with the lower pressure. This causes the high-pressure gas to expand and the low-pressure gas to compress until both gases achieve mechanical equilibrium. At this point, their pressures equalize, and the movement of the wall...