Semi-classical Limit of Confined Fermionic Systems in Homogeneous Magnetic Fields

Fournais, Søren; Madsen, Peter S.

doi:10.1007/s00023-019-00880-6

Cited by 4 publications

(2 citation statements)

References 34 publications

(45 reference statements)

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“…Outline and Sketch of the proof. Our general strategy is inspired by works on mean-field limits for interacting fermions [36,37,38,21,31,59], in particular by the method of [20]. Several improvements are required to handle the singularity of the anyonic Hamiltonian that emerges in the limit R → 0.…”

Section: Model and Main Resultsmentioning

confidence: 99%

Semiclassical Limit for Almost Fermionic Anyons

Girardot

Rougerie

2021

Commun. Math. Phys.

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In two-dimensional space there are possibilities for quantum statistics continuously interpolating between the bosonic and the fermionic one. Quasi-particles obeying such statistics can be described as ordinary bosons and fermions with magnetic interactions. We study a limit situation where the statistics/magnetic interaction is seen as a "perturbation from the fermionic end". We vindicate a mean-field approximation, proving that the ground state of a gas of anyons is described to leading order by a semi-classical, Vlasov-like, energy functional. The ground state of the latter displays anyonic behavior in its momentum distribution. Our proof is based on coherent states, Husimi functions, the Diaconis-Freedman theorem and a quantitative version of a semi-classical Pauli pinciple.

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Section: Model and Main Resultsmentioning

confidence: 99%

Semiclassical Limit for Almost Fermionic Anyons

Girardot

Rougerie

2021

Commun. Math. Phys.

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“…This requires specific methods to couple the two types of limits. A selection of references is [18,19,29,98,212,250,310,110,215,216,217,111,220,174].…”

Section: Connections and Further Topicsmentioning

confidence: 99%

Scaling limits of bosonic ground states, from many-body to non-linear Schrödinger

Rougerie

2021

EMS Surv. Math. Sci.

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How and why could an interacting system of many particles be described as if all particles were independent and identically distributed ? This question is at least as old as statistical mechanics itself. Its quantum version has been rejuvenated by the birth of cold atoms physics. In particular the experimental creation of Bose-Einstein condensates leads to the following variant: why and how can a large assembly of very cold interacting bosons (quantum particles deprived of the Pauli exclusion principle) all populate the same quantum state ?In this text I review the various mathematical techniques allowing to prove that the lowest energy state of a bosonic system forms, in a reasonable macroscopic limit of large particle number, a Bose-Einstein condensate. This means that indeed in the relevant limit all particles approximately behave as if independent and identically distributed, according to a law determined by minimizing a non-linear Schrödinger energy functional. This is a particular instance of the justification of the mean-field approximation in statistical mechanics, starting from the basic many-body Schrödinger Hamiltonian.

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Norm convergence of confined fermionic systems at zero temperature

Cárdenas

2024

Lett Math Phys

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Semi-classical Limit of Confined Fermionic Systems in Homogeneous Magnetic Fields

Cited by 4 publications

References 34 publications

Semiclassical Limit for Almost Fermionic Anyons

Semiclassical Limit for Almost Fermionic Anyons

Scaling limits of bosonic ground states, from many-body to non-linear Schrödinger

Norm convergence of confined fermionic systems at zero temperature

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