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Counting statistics for noninteracting fermions in a d-dimensional potential.
- Source :
-
Physical review. E [Phys Rev E] 2021 Mar; Vol. 103 (3), pp. L030105. - Publication Year :
- 2021
-
Abstract
- 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.
Details
- Language :
- English
- ISSN :
- 2470-0053
- Volume :
- 103
- Issue :
- 3
- Database :
- MEDLINE
- Journal :
- Physical review. E
- Publication Type :
- Academic Journal
- Accession number :
- 33862753
- Full Text :
- https://doi.org/10.1103/PhysRevE.103.L030105