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Updated: May 30, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Published on: December 4, 2017

New field-theoretic method for the virial expansion.

David B Kaplan1, Sichun Sun

  • 1Institute for Nuclear Theory, Box 351550, Seattle, Washington 98195-1550, USA. dbkaplan@uw.edu

Physical Review Letters
|August 16, 2011
PubMed
Summary

We present a new graphical method to calculate virial expansion coefficients for quantum field theories. This approach accurately determines the third virial coefficient for unitary fermions, a complex system.

Area of Science:

  • Quantum Field Theory
  • Statistical Mechanics

Background:

  • Calculating virial expansion coefficients is crucial for understanding the thermodynamic properties of quantum systems.
  • Nonrelativistic quantum field theories, especially those with nonperturbative interactions like unitary fermions, present significant computational challenges.

Purpose of the Study:

  • To develop a novel graphical method for computing virial expansion coefficients in nonrelativistic quantum field theory.
  • To apply this method to calculate the third virial coefficient (b3) for unitary fermions.

Main Methods:

  • A graphical approach is employed to systematically compute contributions to the virial expansion.
  • The method involves calculating specific Feynman-like graphs and performing extrapolations to obtain the coefficients.
  • Applied to unitary fermions, this involves analyzing the interactions of three such particles.

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Main Results:

  • The third virial coefficient (b3) for unitary fermions was computed using the developed graphical method.
  • The calculated value is b3 = -0.2930.
  • This result shows excellent agreement, within 0.7%, with a previous high-precision calculation.

Conclusions:

  • The developed graphical method provides an efficient and accurate way to compute virial coefficients for quantum field theories.
  • The computation for unitary fermions validates the method's applicability to nonperturbative systems.
  • This work offers a new tool for theoretical physics research in many-body systems.