D. B. Gutman

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

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 the 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.

Full Counting Statistics of a Luttinger Liquid Conductor

Nonequilibrium bosonization technique is used to study current fluctuations of interacting electrons in a single-channel quantum wire representing a Luttinger liquid (LL) conductor. An exact expression for the time resolved full counting statistics of the transmitted charge is derived. It is given by the Fredholm determinant of the counting operator with a time-dependent scattering phase. The result has a form of counting statistics of noninteracting particles with fractional charges, induced by scattering off the boundaries between the LL wire and the noninteracting leads.

Shot Noise at High Temperatures

We consider the possibility of measuring nonequilibrium properties of the current correlation functions at high temperatures (and small bias). Through the example of the third cumulant of the current

Anomalous c-axis transport in layered metals.

({\mathcal{S}}_{3})

Coexistence of Coulomb blockade and zero bias anomaly in a strongly coupled nanodot.

we demonstrate that odd-order correlation functions represent nonequilibrium physics even at small external bias and high temperatures. We calculate

Nonequilibrium Luttinger liquid: zero-bias anomaly and dephasing.

{\mathcal{S}}_{3}{=y(eV/T)e}^{2}I

Energy transport in the Anderson insulator

for a quasi-one-dimensional diffusive constriction. We calculate the scaling function y in two regimes: when the scattering processes are purely elastic and when the inelastic electron-electron scattering is strong. In both cases we find that y interpolates between two constants. In the low- (high-) temperature limit y is strongly (weakly) enhanced (suppressed) by the electron-electron scattering.

Tunneling spectroscopy of Luttinger-liquid structures far from equilibrium

Transport in metals with a strongly anisotropic single-particle spectrum is studied. Coherent band transport in all directions, described by the standard Boltzmann equation, is shown to withstand both elastic and inelastic scattering as long as EFtau >> 1. A model of phonon-assisted tunneling via resonant states located in between the layers is suggested to explain a nonmonotonic temperature dependence of the c-axis resistivity observed in experiments.

Cold bosons in the Landauer setup

The current-voltage characteristics through a metallic nanoparticle which is well coupled to a metallic lead are measured. It is shown that the I-V curves are composed of two contributions. One is a suppression of the tunneling conductivity at the Fermi level, and the second is an oscillating feature which shifts with gate voltage. The results indicate that zero-bias anomaly and Coulomb blockade phenomena coexist in an asymmetric strongly coupled zero-dimensional system.

Many-particle correlations in a non-equilibrium Luttinger liquid

A one-dimensional system of interacting electrons out of equilibrium is studied in the framework of the Luttinger liquid model. We analyze several setups and develop a theory of tunneling into such systems. A remarkable property of the problem is the absence of relaxation in energy distribution functions of left and right movers yet the presence of the finite dephasing rate due to electron-electron scattering, which smears zero-bias-anomaly singularities in the tunneling density of states.