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Commutator Estimates for Low-Temperature Fermi Gases
Jacky J. Chong, Laurent Lafleche, Jinyeop Lee, Chiara Saffirio·April 2, 2026
Mathematical Physicsmath.APmath.SPQuantum Physics
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Abstract
We investigate the semiclassical regularity of thermal equilibria in the presence of a harmonic potential at low temperature; that is, we obtain the asymptotic behavior of the Schatten norms of commutators of the one-body operators associated with these equilibria and the position and momentum operators. We also obtain upper bounds in the magnetic field case for the Fock-Darwin Hamiltonian. Our estimates, in particular, allow us to observe several regimes depending on the joint behavior of the Planck constant, the temperature, and the strength of the magnetic field.