Anomalous Hydrodynamics in a One-Dimensional Electronic Fluid.

We construct multimode viscous hydrodynamics for one-dimensional spinless electrons. Depending on the scale, the fluid has six (shortest lengths), four (intermediate, exponentially broad regime), or three (asymptotically long scales) hydrodynamic modes. Interaction between hydrodynamic modes leads to anomalous scaling of physical observables and waves propagating in the fluid. In the four-mode regime, all modes are ballistic and acquire Kardar-Parisi-Zhang (KPZ)-like broadening with asymmetric power-law tails. "Heads" and "tails" of the waves contribute equally to thermal conductivity, leading to ω^{-1/3} scaling of its real part. In the three-mode regime, the system is in the universality class of a classical viscous fluid [O. Narayan and S. Ramaswamy, Anomalous Heat Conduction in One-Dimensional Momentum-Conserving Systems, Phys. Rev. Lett. 89, 200601 (2002).PRLTAO0031-900710.1103/PhysRevLett.89.200601, H. Spohn, Nonlinear fluctuating hydrodynamics for anharmonic chains, J. Stat. Phys. 154, 1191 (2014).JSTPBS0022-471510.1007/s10955-014-0933-y]. Self-interaction of the sound modes results in a KPZ-like shape, while the interaction with the heat mode results in asymmetric tails. The heat mode is governed by Levy flight distribution, whose power-law tails give rise to ω^{-1/3} scaling of heat conductivity.

Thermal Transport in One-Dimensional Electronic Fluids.

We study thermal conductivity for one-dimensional electronic fluids. The many-body Hilbert space is partitioned into bosonic and fermionic sectors that carry the thermal current in parallel. For times shorter than the bosonic umklapp time, the momenta of Bose and Fermi components are separately conserved, giving rise to the ballistic heat propagation and imaginary heat conductivity proportional to T/iω. The real part of thermal conductivity is controlled by decay processes of fermionic and bosonic excitations, leading to several regimes in frequency dependence. At lowest frequencies or longest length scales, the thermal transport is dominated by Lévy flights of low-momentum bosons that lead to a fractional scaling, ω^{-1/3} and L^{1/3}, of heat conductivity with the frequency ω and system size L, respectively.

Multiple periodicity in a nanoparticle-based single-electron transistor.

A single-electron transistor is a nano-device with large potential for low-power applications that can be used as logic elements in integrated circuits. In this device, the conductance oscillates with a well-defined period due to the Coulomb blockade effect. By using a unique technique, we explore single-electron transistors based on a single metallic nanoparticle with tunable coupling to electric leads. We demonstrate a unique regime in which the transistor is characterized by multi-periodic oscillations of the conductance with gate voltage where the additional periods are harmonics of the basic periodicity of the Coulomb blockade and their relative strength can be controllably tuned. These harmonics correspond to a charge change on the dot by a fraction of the electron charge. The presence of multiple harmonics makes these transistors potential elements in future miniaturization of nano-sized circuit elements.Single-electron transistors are elements for nanoscale electronics. Employing single-electron transistors based on gold nanoparticles, Bitton et al., report a fabrication technique that allows precise control over the coupling between a nanodot and leads, resulting in new transport characteristics.

Correlations in nonequilibrium Luttinger liquid and singular Fredholm determinants.

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+ÂB[over ^]), where A(ε) and B(t) have multiple discontinuities in energy and time spaces. 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 nonequilibrium Fermi-edge singularities of many-particle correlation functions. As an example, we calculate a two-particle distribution function characterizing genuinely nonequilibrium quantum correlations between left- and right-moving fermions that have left the interaction region.

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

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.

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.

Nonequilibrium Luttinger liquid: zero-bias anomaly and dephasing.

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.

Nonequilibrium zero-bias anomaly in disordered metals.

We extend the theory of a zero-bias anomaly (ZBA) in the tunneling density of states of a diffusive metallic film to out-of-equilibrium conditions. An effective action describing virtual fluctuations out of equilibrium is derived. The singular behavior of the equilibrium ZBA is smoothed out by real processes of inelastic scattering.

Anomalous c-axis transport in layered metals.

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.