The semi-classical limit of large fermionic systems

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Standard

The semi-classical limit of large fermionic systems. / Fournais, Søren; Lewin, Mathieu; Solovej, Jan Philip.

In: Calculus of Variations and Partial Differential Equations, Vol. 57, No. 4, 105, 2018.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Fournais, S, Lewin, M & Solovej, JP 2018, 'The semi-classical limit of large fermionic systems', Calculus of Variations and Partial Differential Equations, vol. 57, no. 4, 105. https://doi.org/10.1007/s00526-018-1374-2

APA

Fournais, S., Lewin, M., & Solovej, J. P. (2018). The semi-classical limit of large fermionic systems. Calculus of Variations and Partial Differential Equations, 57(4), [105]. https://doi.org/10.1007/s00526-018-1374-2

Vancouver

Fournais S, Lewin M, Solovej JP. The semi-classical limit of large fermionic systems. Calculus of Variations and Partial Differential Equations. 2018;57(4). 105. https://doi.org/10.1007/s00526-018-1374-2

Author

Fournais, Søren ; Lewin, Mathieu ; Solovej, Jan Philip. / The semi-classical limit of large fermionic systems. In: Calculus of Variations and Partial Differential Equations. 2018 ; Vol. 57, No. 4.

Bibtex

@article{9c82b08207b44f9bbc97c5e06a78394a,
title = "The semi-classical limit of large fermionic systems",
abstract = "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.",
author = "S{\o}ren Fournais and Mathieu Lewin and Solovej, {Jan Philip}",
year = "2018",
doi = "10.1007/s00526-018-1374-2",
language = "English",
volume = "57",
journal = "Calculus of Variations and Partial Differential Equations",
issn = "0944-2669",
publisher = "Springer",
number = "4",

}

RIS

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