The semi-classical limit of large fermionic systems

TY - JOUR

T1 - The semi-classical limit of large fermionic systems

AU - Fournais, Søren

AU - Lewin, Mathieu

AU - Solovej, Jan Philip

PY - 2018/8/1

Y1 - 2018/8/1

N2 - We study a system of N fermions in the regime where the intensity of the interaction scales as 1 / N and with an effective semi-classical parameter ħ= N-1/d where d is the space dimension. For a large class of interaction potentials and of external electromagnetic fields, we prove the convergence to the Thomas–Fermi minimizers in the limit N→ ∞. The limit is expressed using many-particle coherent states and Wigner functions. The method of proof is based on a fermionic de Finetti–Hewitt–Savage theorem in phase space and on a careful analysis of the possible lack of compactness at infinity.

AB - We study a system of N fermions in the regime where the intensity of the interaction scales as 1 / N and with an effective semi-classical parameter ħ= N-1/d where d is the space dimension. For a large class of interaction potentials and of external electromagnetic fields, we prove the convergence to the Thomas–Fermi minimizers in the limit N→ ∞. The limit is expressed using many-particle coherent states and Wigner functions. The method of proof is based on a fermionic de Finetti–Hewitt–Savage theorem in phase space and on a careful analysis of the possible lack of compactness at infinity.

U2 - 10.1007/s00526-018-1374-2

DO - 10.1007/s00526-018-1374-2

M3 - Journal article

SN - 0944-2669

VL - 57

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 4

M1 - 105

ER -