# 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 } }

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…

## 19 Citations

### The hard-to-soft edge transition: Exponential moments, central limit theorems and rigidity

- MathematicsJournal of Approximation Theory
- 2022

### Counting statistics for noninteracting fermions in a rotating trap

- PhysicsPhysical Review A
- 2022

We study the ground state of N (cid:29) 1 noninteracting fermions in a two-dimensional harmonic trap rotating at angular frequency Ω > 0. The support of the density of the Fermi gas is a disk of…

### Full counting statistics for interacting trapped fermions

- PhysicsSciPost Physics
- 2021

<jats:p>We study <jats:inline-formula><jats:alternatives><jats:tex-math>N</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"…

### Gap Probability for the Hard Edge Pearcey Process

- MathematicsAnnales Henri Poincaré
- 2023

The hard edge Pearcey process is universal in random matrix theory and many other stochastic models. This paper deals with the gap probability for the thinned/unthinned hard edge Pearcey process over…

### Toeplitz determinants with a one-cut regular potential and Fisher--Hartwig singularities I. Equilibrium measure supported on the unit circle

- Mathematics
- 2022

We consider Toeplitz determinants whose symbol has: (i) a one-cut regular potential V , (ii) Fisher–Hartwig singularities, and (iii) a smooth function in the background. The potential V is associated…

### Disk counting statistics near hard edges of random normal matrices: the multi-component regime

- Mathematics, Computer Science
- 2022

The “hard edge regime” where all disk boundaries are a distance of order 1 n away from the hard wall, where n is the number of points and the asymptotics of the moment generating function are of the form exp.

### Finiteness of entanglement entropy in collective field theory

- PhysicsJournal of High Energy Physics
- 2022

Abstract
We explore the question of finiteness of the entanglement entropy in gravitational theories whose emergent space is the target space of a holographic dual. In the well studied duality of…

### Exponential moments for disk counting statistics at the hard edge of random normal matrices

- Mathematics, Computer Science
- 2022

It is proved that the moment generating function of the disk counting statistics of a model Mittag-Leﬄer ensemble in the presence of a hard wall enjoys asymptotics of the form the semi-hard edge.

### Unified Light-Matter Floquet Theory and its Application to Quantum Communication

- Physics
- 2022

Periodically-driven quantum systems can exhibit a plethora of intriguing non-equilibrium phenomena, that can be analyzed using Floquet theory. Naturally, Floquet theory is employed to describe the…

### On the characteristic polynomial of the eigenvalue moduli of random normal matrices

- Mathematics
- 2022

We study the characteristic polynomial p n ( x ) = Q n j =1 ( | z j | − x ) where the z j are drawn from the Mittag-Leﬄer ensemble, i.e. a two-dimensional determinantal point process which…

## References

SHOWING 1-10 OF 80 REFERENCES

### Noninteracting fermions at finite temperature in a d -dimensional trap: Universal correlations

- Physics
- 2016

We study a system of $N$ non-interacting spin-less fermions trapped in a confining potential, in arbitrary dimensions $d$ and arbitrary temperature $T$. The presence of the trap introduces an edge…

### Statistics of the maximal distance and momentum in a trapped Fermi gas at low temperature

- Physics
- 2016

We consider N non-interacting fermions in an isotropic d-dimensional harmonic trap. We compute analytically the cumulative distribution of the maximal radial distance of the fermions from the trap…

### Entanglement and particle correlations of Fermi gases in harmonic traps

- Physics
- 2012

We investigate quantum correlations in the ground state of noninteracting
Fermi gases of N particles trapped by an external space-dependent harmonic
potential, in any dimension. For this purpose,…

### Point processes in arbitrary dimension from fermionic gases, random matrix theory, and number theory

- Mathematics
- 2008

It is well known that one can map certain properties of random matrices, fermionic gases, and zeros of the Riemann zeta function to a unique point process on the real line . Here we analytically…

### Noninteracting fermions in a trap and random matrix theory

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2019

We review recent advances in the theory of trapped fermions using techniques borrowed from random matrix theory (RMT) and, more generally, from the theory of determinantal point processes. In the…

### Universal ground-state properties of free fermions in a d-dimensional trap

- PhysicsEPL (Europhysics Letters)
- 2015

The ground-state properties of N spinless free fermions in a d-dimensional confining potential are studied. We find that any n-point correlation function has a simple determinantal structure that…

### Quantum fluctuations of one-dimensional free fermions and Fisher–Hartwig formula for Toeplitz determinants

- Mathematics
- 2011

We revisit the problem of finding the probability distribution of a fermionic number of one-dimensional spinless free fermions on a segment of a given length. The generating function for this…

### Non-interacting fermions in hard-edge potentials

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2018

We consider the spatial quantum and thermal fluctuations of non-interacting Fermi gases of N particles confined in d-dimensional non-smooth potentials. We first present a thorough study of the…

### Entanglement entropy and quantum field theory

- Physics
- 2004

We carry out a systematic study of entanglement entropy in relativistic quantum field theory. This is defined as the von Neumann entropy SA = −Tr ρAlogρA corresponding to the reduced density matrix…

### Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains

- PhysicsSciPost Physics
- 2020

We consider an integrable system of two one-dimensional fermionic
chains connected by a link. The hopping constant at the link can be
different from that in the bulk. Starting from an initial state…