Work

Exact first-order effect of interactions on the ground-state energy of harmonically-confined fermions

Year: 2024

Type: article

Abstract: We consider a system of N N spinless fermions, interacting with each other via a power-law interaction \epsilon/r^n ϵ / r n , and trapped in an external harmonic potential V(r) = r^2/2 V ( r ) = r 2 / 2 , in d=1,2,3 d = 1 , 2 , 3 dimensions. For any 0 < n < d+2 0 < n < d + 2 , we obtain the ground-state energy E_N E N of the system perturbatively in \epsilon ϵ , E_{N}=E_{N}^{≤ft(0)}+\epsilon E_{N}^{≤ft(1)}+O≤ft(\epsilon^{2}) E N = E N ≤ f t ( 0 ) + ϵ E N ≤ f t ( 1 ) + O ≤ f t ( ϵ 2 ) . We calculate E_{N}^{≤ft(1)} E N ≤ f t ( 1 ) exactly, assuming that N N is such that the “outer shell” is filled. For the case of n=1

Source: SciPost Physics

DOI: 10.21468/scipostphys.17.2.038

Authors: Pierre Le Doussal, Naftali R. Smith, Nathan Argaman

Institutions: École Normale Supérieure - PSL, Laboratoire de Physique de l'Ecole Normale Supérieure, Ben-Gurion University of the Negev, Shimon Peres Negev Nuclear Research Center

Language: Latvian

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, Israel Science Foundation, Kavli Institute for Theoretical Physics, University of California, Santa Barbara