Volume 113, Number 1, January 2016
|Number of page(s)||6|
|Section||Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties|
|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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.