Related Experiment Video
Updated: Aug 10, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Low-dimensional bose liquids: beyond the gross-pitaevskii approximation
1Department of Physics, University of Virginia, McCormick Road, Charlottesville, Virginia 22903, USA.
Physical Review Letters
|September 16, 2000
Summary
The Gross-Pitaevskii approximation fails for low-dimensional Bose condensates with repulsive interactions. This study proposes universal modifications for these systems, analyzing properties like solitons in one dimension.
Area of Science:
- Quantum mechanics
- Condensed matter physics
- Bose-Einstein condensates
Background:
- The Gross-Pitaevskii approximation is a standard theory for dilute Bose condensates.
- It is widely applied to describe properties of trapped alkali gases.
Purpose of the Study:
- To identify the limitations of the Gross-Pitaevskii approximation in low dimensions (d ≤ 2) for repulsive interactions.
- To propose universal, low-dimensional modifications to the theory.
- To analyze the behavior of one-dimensional Bose condensates using these modifications.
Main Methods:
- Theoretical analysis of the Gross-Pitaevskii equation.
- Development of modified equations for low-dimensional systems.
- Investigation of density profiles, superfluidity, solitons, and self-similar solutions in one dimension.
Main Results:
- The Gross-Pitaevskii approximation is shown to fail for short-ranged repulsive interactions in dimensions d ≤ 2.
- Universal modifications for low-dimensional systems are proposed.
- Detailed analysis of one-dimensional systems reveals specific behaviors of density profiles, superfluid properties, solitons, and self-similar solutions.
Conclusions:
- The proposed modifications are essential for accurately describing low-dimensional Bose condensates with repulsive interactions.
- The findings provide a more accurate theoretical framework for studying systems like trapped alkali gases in reduced dimensions.
Related Concept Videos
04:01Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation
Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws.
02:26Molecular Comparison of Gases, Liquids, and Solids
Particles in a solid are tightly packed together (fixed shape) and often arranged in a regular pattern; in a liquid, they are close together with no regular arrangement (no fixed shape); in a gas, they are far apart with no regular arrangement (no fixed shape). Particles in a solid vibrate about fixed positions (cannot flow) and do not generally move in relation to one another; in a liquid, they move past each other (can flow) but remain in essentially constant contact; in a gas, they move...
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...
01:18pV-Diagrams
The pV diagram, which is a graph of pressure versus volume of the gas under study, is helpful in describing certain aspects of the substance. When the substance behaves like an ideal gas, the ideal gas equation describes the relationship between its pressure and volume. On a pV diagram, it is common to plot an isotherm, which is a curve showing p as a function of V with the number of molecules and the temperature fixed. Then, for an ideal gas, the product of the pressure of the gas and its...
01:29Nonideal Two-Component Liquid Solutions
Nonideal liquid solutions, also known as real solutions, do not strictly follow Raoult's law. Raoult's law is a rule of thumb in physical chemistry. However, not all mixtures adhere to this law due to varying molecular interactions. For example, in an acetone/chloroform solution, the individual vapor pressures of the components are lower than expected, resulting in a total vapor pressure below that predicted by Raoult's law, causing a negative deviation.On the other hand, in an ethanol/water...
01:15Dimensionless Groups in Fluid Mechanics
Dimensionless groups in fluid mechanics provide simplified ratios that help analyze fluid behavior without relying on specific units. The Reynolds number (Re), which represents the ratio of inertial to viscous forces, distinguishes between laminar and turbulent flows, making it essential in the design of pipelines and aerodynamic surfaces. The Froude number (Fr), the ratio of inertial to gravitational forces, is particularly useful in predicting wave formation and hydraulic jumps in...