Year: 2024
Type: article
Abstract: We study the ground state energy of a gas of N fermions confined to a unit box in d dimensions. The particles interact through a two-body potential with strength scaled in an N-dependent way as $$N^{-\alpha }v$$ N - α v , where $$\alpha \in \mathbb {R}$$ α ∈ R and v is a function of positive type satisfying a mild regularity assumption. Our focus is on the strongly interacting case $$\alpha <1-\frac{2}{d}$$ α < 1 - 2 d . We contrast our result with existing results in the weakly interacting case $$\alpha >1-\frac{2}{d}$$ α > 1 - 2 d and the transition happening at the mean-field scaling $$\alpha =1-\frac{2}{d}$$ α = 1 - 2 d . Our proof is an adaptation of the bosonization technique used to treat the mean-field case.
Source: Annales Henri Poincaré
Institution: University of Copenhagen
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W4404061204