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<p>In this paper, we study a gas of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(N \gg 1 \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>≫</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> weakly interacting fermions. We describe the time evolution of states that are perturbations of the Fermi ball, and analyze the dynamics in particle-hole variables. Our main result states that, for small values of the coupling constant and for appropriate initial data, the effective dynamics of the momentum distribution is determined by a discrete collision operator of quantum Boltzmann form.</p>

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Quantum Boltzmann Dynamics and Bosonized Particle-Hole Interactions in Fermion Gases

  • 期刊论文

  • 发表日期：

    2025年12月19日

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  • Esteban Cárdenas,
  • Thomas Chen

摘要

In this paper, we study a gas of \(N \gg 1 \) N ≫ 1 weakly interacting fermions. We describe the time evolution of states that are perturbations of the Fermi ball, and analyze the dynamics in particle-hole variables. Our main result states that, for small values of the coupling constant and for appropriate initial data, the effective dynamics of the momentum distribution is determined by a discrete collision operator of quantum Boltzmann form.