arXiv subjects

Thomas Gamet

Publications and source records attributed to Thomas Gamet.

3 recordsLinked to original sources

arXiv2026

Semi-classical limit of an attractive Fermi gas in one or two dimensions

We study the ground-state of a Fermi gas with short range attrative interactions in one or two dimensions. N fermions are placed in a confining potential, and interact with each other through a negative potential, whose range is larger than the typical distance between particles. We show the convergence of the ground state energy of the Hamiltonian to a Thomas-Fermi energy in the large N limit. Furthermore, we prove convergence of the ground states, in the sense of their Husimi functions. These results extend to the case of a repulsive interaction of positive Fourier transform.

math-ph↗

arXiv2025

Ground state energy of a dilute inhomogeneous Fermi gas

We study the ground state energy of a system of N fermions with two spin states in the large N limit. The particles are placed in an inhomogeneous trapping potential and interact via scaled interactions. We study a dilute limit where the range of the interaction potential is much smaller than the typical inter-particle distance. We show that the energy per particle converges to the Thomas-Fermi energy of the system, with a perturbative term corresponding tot he interaction and exhibiting the scattering length of the potential. The proof is decomposed into two bounds. First, we construct an appropriate test-state to prove the upper bound. Then, we prove the lower bound by the Dyson lemma, which allows us to regularize the interaction potential, and several semi-classical tools.

math-ph↗

arXiv2025

Renormalization of bosonic quadratic Hamiltonians involving rank-one perturbations

We study the renormalization of a bosonic quadratic Hamiltonian with an ultraviolet divergence. The Hamiltonian is composed of the sum of a free part and the square of the smeared field operator. We explicitly diagonalize the Hamiltonian via Bogoliubov transformations, thus simplifying its definition as a self-adjoint operator. Depending on the field operator's smearing, we discuss different renormalizations, either of the energy alone, or the energy and coupling constant together.

math-ph↗