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Related Experiment Video

Updated: May 18, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Virial expansion coefficients in the harmonic approximation.

J R Armstrong1, N T Zinner, D V Fedorov

  • 1Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

This study applies the virial expansion method to interacting identical fermions, calculating partition functions for two and three particles. Results reveal how temperature and interactions affect virial coefficients, offering insights into quantum systems.

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Last Updated: May 18, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy
09:43

Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy

Published on: August 13, 2019

Area of Science:

  • Quantum Many-Body Physics
  • Statistical Mechanics
  • Condensed Matter Theory

Background:

  • The virial expansion is a powerful tool for describing interacting systems, particularly at finite temperatures.
  • Understanding the behavior of identical fermions is crucial in various fields, from nuclear physics to condensed matter.
  • Previous studies often focused on specific limits or simplified models, leaving gaps in the understanding of interacting fermion systems across different regimes.

Purpose of the Study:

  • To apply the virial expansion method within a harmonic approximation to an interacting N-body system of identical fermions.
  • To compute the canonical partition functions for two and three particles, determining the two lowest orders of the virial expansion.
  • To investigate the influence of temperature, dimensionality, and interactions on the virial coefficients.

Main Methods:

  • Utilized the virial expansion method.
  • Employed a harmonic approximation for the N-body system.
  • Calculated canonical partition functions for two and three-fermion systems.
  • Interpolated the energy spectrum to connect low-temperature ground-state properties with high-temperature non-interacting limits.

Main Results:

  • Derived the first two orders of the virial expansion for interacting identical fermions.
  • Demonstrated that the energy spectrum interpolation reproduces key physical limits.
  • Presented numerical results for the second and third virial coefficients, analyzing their dependence on dimension, temperature, interaction strength, and transition temperatures.

Conclusions:

  • The virial expansion, combined with harmonic approximation and careful energy spectrum interpolation, provides a robust framework for studying interacting fermion systems.
  • The calculated virial coefficients offer quantitative insights into the transition from low- to high-energy behaviors, influenced by system parameters.
  • The findings highlight the smearing of shell effects with increasing temperature, a phenomenon relevant to finite quantum systems.