Ground-state energy of one-dimensional free Fermi gases in the thermodynamic limit

الأصل · EN

We study the ground-state energy of one-dimensional, non-interacting fermions subject to an external potential in the thermodynamic limit. To this end, we fix some (Fermi) energy ν>0, confine fermions with total energy below ν inside the interval [-L,L] and study the shift of the ground-state energy due to the potential V in the thermodynamic limit L→∞. We show that the difference Eₗ(ν) of the two ground-state energies with and without potential can be decomposed into a term of order one (leading to the Fumi-term) and a term of order 1/L, which yields the so-called finite size energy. We compute both terms for all possible boundary conditions explicitly and express them through the scattering data of the one-particle Schrödinger operator -Δ+V on L²(R).