# Counting statistics for noninteracting fermions in a d-dimensional potential.

```@article{Smith2020CountingSF,
title={Counting statistics for noninteracting fermions in a d-dimensional potential.},
author={Naftali R. Smith and Pierre Le Doussal and Satya N. Majumdar and Gr{\'e}gory Schehr},
journal={Physical review. E},
year={2020},
volume={103 3},
pages={
L030105
}
}```
• Published 3 August 2020
• Physics
• Physical review. E
We develop a first-principles approach to compute the counting statistics in the ground state of N noninteracting spinless fermions in a general potential in arbitrary dimensions d (central for d>1). In a confining potential, the Fermi gas is supported over a bounded domain. In d=1, for specific potentials, this system is related to standard random matrix ensembles. We study the quantum fluctuations of the number of fermions N_{D} in a domain D of macroscopic size in the bulk of the support. We…
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