Fermionic full counting statistics with smooth boundaries: from discrete particles to bosonization

Abstract

We revisit the problem of full counting statistics of particles on a segment of a one-dimensional gas of free fermions. Using a combination of analytical and numerical methods, we study the crossover between the counting of discrete particles and of the continuous particle density as a function of smoothing in the counting procedure. In the discrete-particle limit, the result is given by the Fisher--Hartwig expansion for Toeplitz determinants, while in the continuous limit we recover the bosonization results. This example of full counting statistics with smoothing is also related to orthogonality catastrophe, Fermi-edge singularity and non-equilibrium bosonization.

7 pages, 4 figures

References in corpus (6)

• Minimal excitation states of electrons in one-dimensional wires
• Universal corrections to scaling for block entanglement in spin-1/2 XX chains
• Non-equilibrium 1D many-body problems and asymptotic properties of Toeplitz determinants
• Shot noise thermometry of the quantum Hall edge states
• Counting Statistics and Dephasing Transition in an Electronic Mach-Zehnder Interferometer
• Fermi-edge singularity in chiral one-dimensional systems far from equilibrium

Cited by in corpus (4)

• Universal many-body response of heavy impurities coupled to a Fermi sea
• Half-integer charge injection by a Josephson junction without excess noise
• Limitations of Caldeira-Leggett model for description of phase transitions in superconducting circuits
• Counting interacting electrons in one dimension