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Foundations of Physics

Reconciling Kinetic and Quantum Theory

Bernard Gaveau, Lawrence S. Schulman

Published Jan 2, 2020• 3 citations
Publisher

Abstract

Abstract We show that in a dilute gas the wave function’s spreading is limited by scattering off other particles. This shows that quantum mechanics can be consistent with the kinetic theory of gases.
DOI
10.1007/s10701-019-00317-4

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We compute the viscosity spectral function of the dilute Fermi gas for different values of the s-wave scattering length aaa, including the unitarity limit a→∞a\to\inftya→∞. We perform the calculation in kinetic theory by studying the response to a non-trivial background metric. We find the expected structure consisting of a diffusive peak in the transverse shear channel and a sound peak in the longitudinal channel. At zero momentum the width of the diffusive peak is ω0≃(2ϵ)/(3η)\omega_0\simeq (2\epsilon)/(3\eta)ω0​≃(2ϵ)/(3η) where ϵ\epsilonϵ is the energy density and η\etaη is the shear viscosity. At finite momentum the spectral function approaches the collisionless limit and the width is of order ω0∼k(T/m)1/2\omega_0\sim k(T/m)^{1/2}ω0​∼k(T/m)1/2.
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