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Self-consistent equation for an interacting Bose gas.

Philippe A Martin1, Jaroslaw Piasecki

  • 1Institute of Theoretical Physics, Swiss Federal Institute for Technology Lausanne, CH-1015, Lausanne EPFL, Switzerland. phmartin@dpmail.epfl.ch

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 26, 2003
PubMed
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This study introduces a polymer representation for interacting Bose gases, revealing a self-consistent relation between density and chemical potential. This framework simplifies to free gas behavior in the mean-field limit and offers insights into Bose-Einstein condensation.

Area of Science:

  • Quantum statistical mechanics
  • Condensed matter physics

Background:

  • Interacting Bose gases are fundamental in quantum many-body physics.
  • Understanding their thermodynamic properties, especially near Bose-Einstein condensation, is crucial.

Purpose of the Study:

  • To develop a polymer representation for interacting Bose gases in thermal equilibrium.
  • To establish a self-consistent relation between density and chemical potential.
  • To analyze the mean-field limit and corrections near Bose-Einstein condensation.

Main Methods:

  • Utilizing Feynman-Kac functional integrals to represent the partition function.
  • Applying Mayer graph summation techniques to derive the self-consistent relation.
  • Employing Kac's scaling for the mean-field limit analysis.

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Main Results:

  • A classical-like polymer representation of the quantum gas was established.
  • A self-consistent relation rho(mu)=F(mu-(a)rho(mu)) was demonstrated.
  • In the mean-field limit, the function F simplifies to the free gas density, with tree diagrams dominating.

Conclusions:

  • The polymer representation provides a powerful tool for studying Bose gases.
  • The derived self-consistent relation is valid within Mayer series convergence and extendable beyond.
  • Dominant corrections to the mean field near Bose-Einstein condensation were analyzed.