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.
De Anthony Leverrier
De Zbigniew Puchała
De Benoit Collins
De Satya Majumdar
De Motohisa Fukuda
De Nilanjana Datta
De Daniel Stilck Franca
De Radosław Adamczak
De Madalin Guta
De Antonio Acín
De Ashley Montanaro
De Ping Zhong
De James Mingo
De Camille Male
De Albert Schwarz
De Clément Delcamp
De Clément Delcamp
De Giuseppe Savaré
