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arXiv · 1507.07896

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

Dmitri A. Ivanov·Ivan P. Levkivskyi
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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.

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Dmitri A. Ivanov, Ivan P. Levkivskyi. 2015-07-28. Fermionic full counting statistics with smooth boundaries: from discrete particles to bosonization. https://doi.org/10.1209/0295-5075/113/17009

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