Proposal for non-local electron-hole turnstile in the Quantum Hall regime

We present a theory for a mesoscopic turnstile that produces spatially separated streams of electrons and holes along edge states in the quantum Hall regime. For a broad range of frequencies in the non-adiabatic regime the turnstile operation is found to be ideal, producing one electron and one hole per cycle. The accuracy of the turnstile operation is characterized by the fluctuations of the transferred charge per cycle. The fluctuations are found to be negligibly small in the ideal regime.Comment: 4+ pages, 2 figure

Application of the exact regularized point particle method (ERPP) to particle laden turbulent shear flows in the two-way coupling regime

The Exact Regularized Point Particle method (ERPP), which is a new inter-phase momentum coupling ap- proach, is extensively used for the first time to explore the response of homogeneous shear turbulence in presence of different particle populations. Particle suspensions with different Stokes number and/or mass loading are considered. Particles with Kolmogorov Stokes number of order one suppress turbulent kinetic energy when the mass loading is increased. In contrast, heavier particles leave this observable almost un- changed with respect to the reference uncoupled case. Turbulence modulation is found to be anisotropic, leaving the streamwise velocity fluctuations less affected by unitary Stokes number particles whilst it is increased by heavier particles. The analysis of the energy spectra shows that the turbulence modulation occurs throughout the entire range of resolved scales leading to non-trivial augmentation/depletion of the energy content among the different velocity components at different length-scales. In this regard, the ERPP approach is able to provide convergent statistics up to the smallest dissipative scales of the flow, giving the opportunity to trust the ensuing results. Indeed, a substantial modification of the turbu- lent fluctuations at the smallest-scales, i.e. at the level of the velocity gradients, is observed due to the particle backreaction. Small scale anisotropies are enhanced and fluctuations show a greater level of in- termittency as measured by the probability distribution function of the longitudinal velocity increments and by the corresponding flatness

Quantum heat fluctuations of single particle sources

Optimal single electron sources emit regular streams of particles, displaying no low frequency charge current noise. Due to the wavepacket nature of the emitted particles, the energy is however fluctuating, giving rise to heat current noise. We investigate theoretically this quantum source of heat noise for an emitter coupled to an electronic probe in the hot-electron regime. The distribution of temperature and potential fluctuations induced in the probe is shown to provide direct information on the single particle wavefunction properties and display strong non-classical features.Comment: 5 pages, 2 figure

The Partial Visibility Representation Extension Problem

For a graph $G$, a function $\psi$ is called a \emph{bar visibility representation} of $G$ when for each vertex $v \in V(G)$, $\psi(v)$ is a horizontal line segment (\emph{bar}) and $uv \in E(G)$ iff there is an unobstructed, vertical, $\varepsilon$-wide line of sight between $\psi(u)$ and $\psi(v)$. Graphs admitting such representations are well understood (via simple characterizations) and recognizable in linear time. For a directed graph $G$, a bar visibility representation $\psi$ of $G$, additionally, puts the bar $\psi(u)$ strictly below the bar $\psi(v)$ for each directed edge $(u,v)$ of $G$. We study a generalization of the recognition problem where a function $\psi'$ defined on a subset $V'$ of $V(G)$ is given and the question is whether there is a bar visibility representation $\psi$ of $G$ with $\psi(v) = \psi'(v)$ for every $v \in V'$. We show that for undirected graphs this problem together with closely related problems are \NP-complete, but for certain cases involving directed graphs it is solvable in polynomial time.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Experimental verification of reciprocity relations in quantum thermoelectric transport

Symmetry relations are manifestations of fundamental principles and constitute cornerstones of modern physics. An example are the Onsager relations between coefficients connecting thermodynamic fluxes and forces, central to transport theory and experiments. Initially formulated for classical systems, these reciprocity relations are also fulfilled in quantum conductors. Surprisingly, novel relations have been predicted specifically for thermoelectric transport. However, whereas these thermoelectric reciprocity relations have to date not been verified, they have been predicted to be sensitive to inelastic scattering, always present at finite temperature. The question whether the relations exist in practice is important for thermoelectricity: whereas their existence may simplify the theory of complex thermoelectric materials, their absence has been shown to enable, in principle, higher thermoelectric energy conversion efficiency for a given material quality. Here we experimentally verify the thermoelectric reciprocity relations in a four-terminal mesoscopic device where each terminal can be electrically and thermally biased, individually. The linear response thermoelectric coefficients are found to be symmetric under simultaneous reversal of magnetic field and exchange of injection and emission contacts. Intriguingly, we also observe the breakdown of the reciprocity relations as a function of increasing thermal bias. Our measurements thus clearly establish the existence of the thermoelectric reciprocity relations, as well as the possibility to control their breakdown with the potential to enhance thermoelectric performanceComment: 7 pages, 5 figure

Planar L-Drawings of Directed Graphs

We study planar drawings of directed graphs in the L-drawing standard. We provide necessary conditions for the existence of these drawings and show that testing for the existence of a planar L-drawing is an NP-complete problem. Motivated by this result, we focus on upward-planar L-drawings. We show that directed st-graphs admitting an upward- (resp. upward-rightward-) planar L-drawing are exactly those admitting a bitonic (resp. monotonically increasing) st-ordering. We give a linear-time algorithm that computes a bitonic (resp. monotonically increasing) st-ordering of a planar st-graph or reports that there exists none.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Planar Embeddings with Small and Uniform Faces

Motivated by finding planar embeddings that lead to drawings with favorable aesthetics, we study the problems MINMAXFACE and UNIFORMFACES of embedding a given biconnected multi-graph such that the largest face is as small as possible and such that all faces have the same size, respectively. We prove a complexity dichotomy for MINMAXFACE and show that deciding whether the maximum is at most $k$ is polynomial-time solvable for $k \leq 4$ and NP-complete for $k \geq 5$. Further, we give a 6-approximation for minimizing the maximum face in a planar embedding. For UNIFORMFACES, we show that the problem is NP-complete for odd $k \geq 7$ and even $k \geq 10$. Moreover, we characterize the biconnected planar multi-graphs admitting 3- and 4-uniform embeddings (in a $k$-uniform embedding all faces have size $k$) and give an efficient algorithm for testing the existence of a 6-uniform embedding.Comment: 23 pages, 5 figures, extended version of 'Planar Embeddings with Small and Uniform Faces' (The 25th International Symposium on Algorithms and Computation, 2014

Spectral distribution and wavefunction of electrons emitted from a single particle source in the quantum Hall regime

We investigate theoretically a scheme for spectroscopy of electrons emitted by an on-demand single particle source. The total system, with an electron turnstile source and a single level quantum dot spectrometer, is implemented with edge states in a conductor in the quantum Hall regime. Employing a Floquet scattering approach, the source and the spectrometer are analyzed within a single theoretical framework. The non-equilibrium distribution of the emitted electrons is analyzed via the direct current at the dot spectrometer. In the adiabatic and intermediate source frequency regimes, the distribution is found to be strongly peaked around the active resonant level of the turnstile. At high frequencies the distribution is split up into a set of fringes, resulting from the interplay of resonant transport through the turnstile and absorption or emission of individual Floquet quanta. For ideal source operation, with exactly one electron emitted per cycle, an expression for the single electron wavefunction is derived.Comment: 12 pages, 7 figure

Tuning of the functional beamforming resolution for wind tunnel measurements

Conventional Frequency Domain Beamforming (CB) is characterised by the frequency dependency of the mainlobe width and by the presence of sidelobes that limit its dynamic range. Functional Beamforming (FB) has been introduced with the aim to overcome these limitations, narrowing the mainlobe and reducing the sidelobe levels. This paper introduces a strategy to obtain a beamformer with a target mainlobe width that is constant over a desired frequency range. The idea is to properly adjust the Functional Beamforming order ν, frequency by frequency, to preserve the mainlobe width. A tuning procedure of the order ν is presented and applied to a typical wind tunnel setup. A detailed analysis of the dependency “order ν versus frequency” is discussed and a general formula describing this dependency is provided. Finally, the effectiveness of the proposed approach is shown both on simulated and experimental test case