| Issue |
EPL
Volume 113, Number 1, January 2016
|
|
|---|---|---|
| Article Number | 17009 | |
| Number of page(s) | 6 | |
| Section | Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties | |
| DOI | https://doi.org/10.1209/0295-5075/113/17009 | |
| Published online | 04 February 2016 | |
Fermionic full counting statistics with smooth boundaries: From discrete particles to bosonization
1 Institute for Theoretical Physics, ETH Zürich - 8093 Zürich, Switzerland
2 Institute for Theoretical Physics, University of Zürich - 8057 Zürich, Switzerland
3 Bogolyubov Institute for Theoretical Physics - 14- b Metrolohichna Street, Kyiv 03680, Ukraine
Received: 21 August 2015
Accepted: 14 January 2016
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.
PACS: 71.10.Pm – Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.) / 05.30.Fk – Fermion systems and electron gas / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EPLA, 2016
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