Related papers: Landauer-B\"uttiker and Thouless conductance
We perform first principles numerical simulations to investigate resistance fluctuations in mesoscopic samples, near the transition between consecutive Quantum Hall plateaus. We use six-terminal geometry and sample sizes similar to those of…
We generalize Thouless bandwidth formula to its n-th moment. We obtain a closed expression in terms of polygamma, zeta and Euler numbers.
The two-particle finite-volume scattering formalism derived by L\"uscher and generalized in many subsequent works does not hold for energies far enough below the two-particle threshold to reach the nearest left-hand cut. The breakdown of…
Tichler proved that a manifold admitting a smooth closed one-form fibers over a circle. More generally a manifold admitting $k$ independent closed one-forms fibers over a torus $T^k$. In this article we explain a version of this…
We give a brief introduction to Luttinger liquids and to the phenomena of electronic transport or conductance in quantum wires. We explain why the subject of transport in Luttinger liquids is relevant and fascinating and review some…
Using the self-consistent Hartree-Fock method, we calculate the persistent current of weakly-interacting spinless electrons in a one-dimensional ring containing a single delta-barrier. We find that the persistent current decays with the…
Consider a bunch of interacting electrons confined in a quantum dot. The later is suddenly coupled to semi-infinite biased leads at an initial instant $t=0$. We identify the dominant contribution to the ergodic current in the off-resonant…
Advances in fabrication and control of quantum dots allow the realization of metastructures that may exhibit novel electrical transport phenomena. Here, we investigate the electrical current passing through one such metastructure, a system…
I am concerned in these lectures with the breakdown of the particle concept in strongly correlated electron matter. I first show that the standard procedure for counting particles, namely Luttinger's theorem, breaks down anytime pole-like…
We present a novel way of defining transmission coefficient of one spatial dimensional few interacting electrons system. The formalism is based on the probability interpretation of unitarity of physical scattering $S$-matrix. The relation…
The Landauer formula allows us to describe theoretically the conductance in terms of the transmission function in a mesoscopic system. We propose a general method to evaluate the transmission function in the complex domain for systems…
The 3D incompressible Euler equation is an important research topic in the mathematical study of fluid dynamics. Not only is the global regularity for smooth initial data an open issue, but the behaviour may also depend on the presence or…
We calculate the counting statistics of electron transfer through an open quantum dot with charging interaction. A dot that is connected to leads by two single-channel quantum point contacts in an in-plane magnetic field is described by a…
The generation of entanglement between two oscillators that interact via a common reservoir is theoretically studied. The reservoir is modeled by a one-dimensional harmonic crystal initially in thermal equilibrium. Starting from a separable…
Quantum theory is proposed of high energy electrons scattering in ultrathin crystals. This theory is based upon a special representation of the scattering amplitude in the form of the integral over the surface surrounding the crystal, and…
Motivated by the Onsager statistical mechanics description of turbulent Euler flows with point singularities, we make a first step in the generalization of the mean field theory in [Caglioti, Lions, Marchioro, Pulvirenti; Comm. Math. Phys.…
In the ballistic limit, the Landauer conductance steps of a mesoscopic quantum wire have been explained by coherent and dissipationless transmission of individual electrons across a one-dimensional barrier. This leaves untouched the central…
Recent advances in nano-thermometry motivate the extension of the Landauer-B\"uttiker scattering theory as to include the non-local dissipation associated with charge transport. Such a program is implemented by describing the inelastic…
The Landauer formula for electrical conductance is simple but works remarkably well in mesoscopic systems. We propose a Landauer-like formula for calculating an escape rate out of a dissipative metastable well, the quantum Kramers rate.
Hydrodynamic electron flow is experimentally observed in the differential resistance of electrostatically defined wires in the two-dimensional electron gas in (Al,Ga)As heterostructures. In these experiments current heating is used to…