1–26 Apr 2019
Nordita, Stockholm
Europe/Stockholm timezone

Rotating trapped fermions in 2d and the complex Ginibre ensemble

24 Apr 2019, 15:00
1h
122:026 (Nordita, Stockholm)

122:026

Nordita, Stockholm

Speaker

Satyanarayan Majumdar

Description

Satyanarayan Majumdar, LPTMS, Universite Paris-Sud, Orsay
Rotating trapped fermions in 2d and the complex Ginibre ensemble

We establish an exact mapping between the positions of N noninteracting fermions in a 2d rotating harmonic trap in its ground-state and the eigenvalues of the NxN complex Ginibre ensemble of Random Matrix Theory (RMT). Using RMT techniques, we make precise predictions for the statistics of the positions of the fermions, both in the bulk as well as at the edge of the trapped Fermi gas. In addition, we compute exactly, for any finite N, the Renyi entanglement entropy and the number variance of a disk of radius r in the ground-state. We show that while these two quantities are proportional to each other in the (extended) bulk, this is no longer the case very close to the trap center nor at the edge. Near the edge, and for large N, we provide exact expressions for the scaling functions associated with these two observables.

Primary author

Prof. Satyanarayan Majumdar

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