Commutator Estimates for Low-Temperature Fermi Gases

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.

Source: arXiv:2604.02297v1 - http://arxiv.org/abs/2604.02297v1 PDF: https://arxiv.org/pdf/2604.02297v1 Original Link: http://arxiv.org/abs/2604.02297v1