Related Experiment Video
Updated: Jun 14, 2026
07:46
Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
Condensate density of interacting bosons: A functional renormalization group approach
Christopher Eichler1, Nils Hasselmann, Peter Kopietz
1Institut für Theoretische Physik, Universität Frankfurt, Max-von-Laue-Strasse 1, 60438 Frankfurt, Germany.
Summary
We used the functional renormalization group (FRG) to calculate the temperature-dependent condensate density of interacting bosons. Results align with XY-universality class predictions, offering insights into quantum systems.
Area of Science:
- Quantum many-body physics
- Condensed matter theory
- Statistical mechanics
Background:
- Understanding the behavior of interacting bosons is crucial for various quantum phenomena.
- The condensate density is a key order parameter in systems exhibiting Bose-Einstein condensation.
- Previous studies often relied on approximations that may limit accuracy.
Purpose of the Study:
- To calculate the temperature-dependent condensate density of interacting bosons in three dimensions.
- To determine the order parameter exponent near the critical point.
- To investigate the effect of higher-order terms in the effective potential on condensate density in two dimensions.
Main Methods:
- Employing the functional renormalization group (FRG) approach.
- Solving truncated FRG flow equations for irreducible vertices numerically.
- Extrapolating numerical results to the critical point.
- Utilizing a derivative expansion including cubic and quartic terms for two-dimensional calculations.
Main Results:
- Obtained temperature-dependent condensate density rho0(T) for interacting bosons in 3D.
- Determined the order parameter exponent beta to be approximately 0.32, consistent with XY-universality.
- Calculated the 2D condensate density at zero temperature, showing small corrections from cubic and quartic terms.
Conclusions:
- The functional renormalization group provides an accurate method for studying boson condensates.
- The calculated exponent supports the applicability of XY-universality to these systems.
- Higher-order terms in the effective potential have a minor impact on the condensate density in 2D.
More Related Videos
Related Concept Videos
01:28Debye–Huckel–Onsager Conductance Equation
The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
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...
01:15Dimensionless 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...
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.
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,...
00:56Density
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...