The semi-classical limit of large fermionic systems
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The semi-classical limit of large fermionic systems. / Fournais, Søren; Lewin, Mathieu; Solovej, Jan Philip.
I: Calculus of Variations and Partial Differential Equations, Bind 57, Nr. 4, 105, 2018.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - The semi-classical limit of large fermionic systems
AU - Fournais, Søren
AU - Lewin, Mathieu
AU - Solovej, Jan Philip
PY - 2018
Y1 - 2018
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 $\hbar=N^{-1/d}$ 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 $N\to\infty$. 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 $\hbar=N^{-1/d}$ 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 $N\to\infty$. 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
VL - 57
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
SN - 0944-2669
IS - 4
M1 - 105
ER -
ID: 152935146