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arXiv · 1212.0708

Correlations in non-equilibrium Luttinger liquid and singular Fredholm determinants

I. V. Protopopov·D. B. Gutman·A. D. Mirlin
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Abstract

We study interaction-induced correlations in Luttinger liquid with multiple Fermi edges. Many-particle correlation functions are expressed in terms of Fredholm determinants ${\rm det}(1+\hat{A}\hat{B})$, where $A(\epsilon)$ and $B(t)$ have multiple discontinuities in energy and time spaces. Such determinants are a generalization of Toeplitz determinants with Fisher-Hartwig singularities. We propose a general asymptotic formula for this class of determinants and provide analytical and numerical support to this conjecture. This allows us to establish non-equilibrium power-law singularities of many-particle correlation functions. As an example, we calculate a two-particle distribution function characterizing correlations between left- and right-moving fermions that have left the interaction region.

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I. V. Protopopov, D. B. Gutman, A. D. Mirlin. 2012-12-04. Correlations in non-equilibrium Luttinger liquid and singular Fredholm determinants. https://doi.org/10.1103/physrevlett.110.216404

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