Non-equilibrium 1D many-body problems and asymptotic properties of Toeplitz determinants

Abstract

Non-equilibrium bosonization technique facilitates the solution of a number of important many-body problems out of equilibrium, including the Fermi-edge singularity, the tunneling spectroscopy and full counting statistics of interacting fermions forming a Luttinger liquid. We generalize the method to non-equilibrium hard-core bosons (Tonks-Girardeau gas) and establish interrelations between all these problems. The results can be expressed in terms of Fredholm determinants of Toeplitz type. We analyze the long time asymptotics of such determinants, using Szegő and Fisher-Hartwig theorems. Our analysis yields dephasing rates as well as power-law scaling behavior, with exponents depending not only on the interaction strength but also on the non-equilibrium state of the system.

13 pages, 3 figures

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• Fermi Edge Resonances in Non-equilibrium States of Fermi Gases
• Transient Features in Charge Fractionalization, Local Equilibration and Non-equilibrium Bosonization
• On Landauer--Büttiker formalism from a quantum quench
• Fermi edge singularity and finite frequency spectral features in a semi-infinite 1D wire
• Asymptotic behaviour of determinants through the expansion of the Moyal star product
• Fate of the Quasi-condensed State for Bias-driven Hard-Core Bosons in one Dimension