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Applications of NonCommutative Geometry to Gauge Theories, Field Theories, and Quantum Space-Time / Applications de la Géométrie Non Commutative aux Théories de Jauge, à la Théorie des Champs et aux Espaces-Temps Quantiques

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2017 - T3 - WS2 - Probabilistic techniques and quantum information theory

Collection 2017 - T3 - WS2 - Probabilistic techniques and quantum information theory

Organizer(s) Lancien, Cécilia ; Nechita, Ion ; Życzkowski, Karol
Date(s) 23/10/2017 - 27/10/2017
linked URL https://web.archive.org/web/20201010200043/https://sites.google.com/site/analysisqit2017/main-events/workshop2
00:00:00 / 00:00:00
7 26

Number variance and entanglement entropy of trapped fermions via random matrix theory

By Satya Majumdar

Consider N free Fermions in a one dimensional harmonic trap. How many Fermions are there at zero temperature in an interval [-L,L]? The ground state quantum fluctuations of the number of Fermions in [-L,L] can be mapped to the classical fluctutions of the number of eigenvalues in [-L,L] of a Gaussian random Hermitian matrix with complex entries. This mapping allows us to compute exactly for large N, using a Coulomb gas approach, the variance of number of Fermions in the quantum system at T=0, as a function of L. The variance exhibits, as a function of L, a very interesting non-monotonic behaviour. I'll then discuss how these results can be used to compute also the ground state entanglement entropy of the interval [-L,L] with the rest of the system.

Information about the video

  • Date of recording 23/10/2017
  • Date of publication 31/10/2017
  • Institution IHP
  • Licence CC BY-NC-ND
  • Language English
  • Format MP4

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