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… 

Figures from this paper

Counting statistics for noninteracting fermions in a rotating trap

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

<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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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
...