Mesoscopic Transport: The Electron-Gas Sum Rules in a Driven Quantum Point Contact

Electron transport in mesoscopic conductors has traditionally involved investigations of the mean current and the fluctuations of the current. A complementary view on charge transport is provided by the distribution of waiting times between charge carriers, but a proper theoretical framework for coherent electronic systems has so far been lacking. Here we develop a quantum theory of electron waiting times in mesoscopic conductors expressed by a compact determinant formula. We...

Strongly interacting electrons can move in a neatly coordinated way, reminiscent of the movement of viscous fluids. Here we show that in viscous flows interactions facilitate transport, allowing conductance to exceed the fundamental Landauer's ballistic limit $G_{\rm ball}$. The effect is particularly striking for the flow through a viscous point contact, a constriction exhibiting the quantum-mechanical ballistic transport at $T=0$ but governed by electron hydrodynamics at el...

How dissipation affects transport is an important theme in quantum science. Here we theoretically investigate an impact of a single-particle loss in mesoscopic transport, which has been an issue in experiments of ultracold atomic gases. By explicitly analyzing quantum point contact and quantum dot systems, we obtain a cumulant generating function on the particle current whose formal expression turns out to be common to two systems. In terms of this generating function, behavi...

We present an approach to steady-state mesoscopic transport based on the maximum entropy principle formulation of nonequilibrium statistical mechanics. This approach is valid in the nonlinear regime of high current, and yields the quantization observed in the integer quantum Hall effect at large currents. A key ingredient of this approach, and its success in explaining high-precision Hall measurements, is that the occupancy of single-electron states depends on their current a...

The $f$-sum rule and the Kohn formula are well-established general constraints on the electric conductivity in quantum many-body systems. We present their generalization to non-linear conductivities at all orders of the response in a unified manner, by considering two limiting quantum time-evolution processes: a quench process and an adiabatic process. Our generalized formulas are valid in any stationary state, including the ground state and finite temperature Gibbs states, r...

We predict that the mesoscopic tensile force fluctuations in metal quantum point contacts (nanowires) arise as a result of finite electric voltage on the contact. They are due to reconfiguration of the electronic subsystem and are correlated with the nonlinearities of the current-voltage characteristics of the contact. The observation of the effect would directly confirm the recently suggested "free-electron" mechanism of mesoscopic force fluctuations observed in nanowires un...

Experimental progresses in the miniaturisation of electronic devices have made routinely available in the laboratory small electronic systems, on the micron or sub-micron scale, which at low temperature are sufficiently well isolated from their environment to be considered as fully coherent. Some of their most important properties are dominated by the interaction between electrons. Understanding their behaviour therefore requires a description of the interplay between interfe...

A brief overview is presented of recent work which investigates the time-dependent relaxation of charge and its spontaneous fluctuations on mesoscopic conductors in the proximity of gates. The leading terms of the low frequency conductance are determined by a capacitive or inductive emittance and a dissipative charge relaxation resistance. The charge relaxation resistance is determined by the ratio of the mean square dwell time of the carriers in the conductor and the square ...

So far transport properties of nanoscale contacts have been mostly studied within the static scattering approach. The electron dynamics and the transient behavior of current flow, however, remain poorly understood. We present a numerical study of microscopic current flow dynamics in nanoscale quantum point contacts. We employ an approach that combines a microcanonical picture of transport with time-dependent density-functional theory. We carry out atomic and jellium model cal...

Using a hydrodynamic model of the electron fluid in a point contact geometry we show that localized plasmons are likely to exist near the constriction. We attempt to relate these plasmons with the recent experimental observation of deviations of the quantum point contact conductance from ideal integer quantization. As a function of temperature this deviation exhibits an activated behavior, exp(-T_a/T), with a density dependent activation temperature T_a of the order of 2 K. W...