Correlations in non-equilibrium Luttinger liquid and singular Fredholm determinants

Abstract

We study interaction-induced correlations in Luttinger liquid with multiple Fermi edges. Many-particle correlation functions are expressed in terms of Fredholm determinants $\det (1+\hat{A}\hat{B})$, 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.

4 pages + Supplemental material as appendix

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Cited by in corpus (6)

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• Dissipationless kinetics of one dimensional interacting fermions
• Atomtronics with a spin: statistics of spin transport and non-equilibrium orthogonality catastrophe in cold quantum gases
• Interaction-induced charge transfer in a mesoscopic electron spectrometer
• Transient Features in Charge Fractionalization, Local Equilibration and Non-equilibrium Bosonization
• Measuring the Luttinger liquid parameter with shot noise