• DOI:10.1103/PhysRevE.103.L030105
• Corpus ID: 220936581

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
        }
}

• Naftali R. Smith, P. Le Doussal, +1 author G. Schehr
• 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 show that the variance of N_{D} grows as N^{(d-1)/d}(A_{d}logN+B_{d}) for large N, and obtain the explicit dependence of A_{d},B_{d} on the potential and on the size of D (for a spherical domain in d>1). This generalizes the free-fermion results for microscopic domains, given in d=1 by the Dyson-Mehta asymptotics from random matrix theory. This leads us to conjecture similar asymptotics for the entanglement entropy of the subsystem D, in any dimension, supported by exact results for d=1.