Transport properties of partially equilibrated quantum wires

We study the effect of thermal equilibration on the transport properties of a weakly interacting one-dimensional electron system. Although equilibration is severely suppressed due to phase-space restrictions and conservation laws, it can lead to intriguing signatures in partially equilibrated quantum wires. We consider an ideal homogeneous quantum wire. We find a finite temperature correction to the quantized conductance, which for a short wire scales with its length, but saturates to a length-independent value once the wire becomes exponentially long. We also discuss thermoelectric properties of long quantum wires. We show that the uniform quantum wire is a perfect thermoelectric refrigerator, approaching Carnot efficiency with increasing wire length.Comment: 20 pages, 6 figure

Resistivity of inhomogeneous quantum wires

We study the effect of electron-electron interactions on the transport in an inhomogeneous quantum wire. We show that contrary to the well-known Luttinger liquid result, non-uniform interactions contribute substantially to the resistance of the wire. In the regime of weakly interacting electrons and moderately low temperatures we find a linear in T resistivity induced by the interactions. We then use the bosonization technique to generalize this result to the case of arbitrarily strong interactions.Comment: 4 pages, 1 figur

Cooper pair splitting in a nanoSQUID geometry at high transparency

We describe a Josephson device composed of two superconductors separated by two interacting quantum dots in parallel, as a probe for Cooper pair splitting. In addition to sequential tunneling of electrons through each dot, an additional transport channel exists in this system: crossed Andreev reflection, where a Cooper pair from the source is split between the two dots and recombined in the drain superconductor. Unlike non-equilibrium scenarios for Cooper pair splitting which involves superconducting/normal metal "forks", our proposal relies on an Aharonov-Bohm measurement of the DC Josephson current when a flux is inserted between the two dots. We provide a path integral approach to treat arbitrary transparencies, and we explore all contributions for the individual phases ($0$ or $\pi$) of the quantum dots. We propose a definition of the Cooper pair splitting efficiency for arbitrary transparencies, which allows us to find the phase associations which favor the crossed Andreev process. Possible applications to experiments using nanowires as quantum dots are discussed.Comment: 12 pages, 13 figure

Hanbury Brown and Twiss noise correlations in a topological superconductor beam splitter

We study Hanbury-Brown and Twiss current cross-correlations in a three-terminal junction where a central topological superconductor (TS) nanowire, bearing Majorana bound states at its ends, is connected to two normal leads. Relying on a non-perturbative Green function formalism, our calculations allow us to provide analytical expressions for the currents and their correlations at subgap voltages, while also giving exact numerical results valid for arbitrary external bias. We show that when the normal leads are biased at voltages $V_1$ and $V_2$ smaller than the gap, the sign of the current cross-correlations is given by -\mbox{sgn}(V_1 \, V_2). In particular, this leads to positive cross-correlations for opposite voltages, a behavior in stark contrast with the one of a standard superconductor, which provides a direct evidence of the presence of the Majorana zero-mode at the edge of the TS. We further extend our results, varying the length of the TS (leading to an overlap of the Majorana bound states) as well as its chemical potential (driving it away from half-filling), generalizing the boundary TS Green function to those cases. In the case of opposite bias voltages, \mbox{sgn}(V_1 \, V_2)=-1, driving the TS wire through the topological transition leads to a sign change of the current cross-correlations, providing yet another signature of the physics of the Majorana bound state.Comment: 14 pages, 8 figure

Giant shot noise from Majorana zero modes in topological trijunctions

The clear-cut experimental identification of Majorana bound states in transport measurements still poses experimental challenges. We here show that the zero-energy Majorana state formed at a junction of three topological superconductor wires is directly responsible for giant shot noise amplitudes, in particular at low voltages and for small contact transparency. The only intrinsic noise limitation comes from the current-induced dephasing rate due to multiple Andreev reflection processes

Chaining of welding and finish turning simulations for austenitic stainless steel components

The chaining of manufacturing processes is a major issue for industrials who want to understand and control the quality of their products in order to ensure their in-service integrity (surface integrity, residual stresses, microstructure, metallurgical changes, distortions,…). Historically, welding and machining are among the most studied processes and dedicated approaches of simulation have been developed to provide reliable and relevant results in an industrial context with safety requirements. As the simulation of these two processes seems to be at an operationnal level, the virtual chaining of both must now be applied with a lifetime prediction prospect. This paper will first present a robust method to simulate multipass welding processes that has been validated through an international round robin. Then the dedicated “hybrid method”, specifically set up to simulate finish turning, will be subsequently applied to the welding simulation so as to reproduce the final state of the pipe manufacturing and its interaction with previous operations. Final residual stress fields will be presented and compared to intermediary results obtained after welding. The influence of each step on the final results will be highlighted regarding surface integrity and finally ongoing validation works and numerical modeling enhancements will be discussed

Two-scale composite finite element method for Dirichlet problems on complicated domains

In this paper, we define a new class of finite elements for the discretization of problems with Dirichlet boundary conditions. In contrast to standard finite elements, the minimal dimension of the approximation space is independent of the domain geometry and this is especially advantageous for problems on domains with complicated micro-structures. For the proposed finite element method we prove the optimal-order approximation (up to logarithmic terms) and convergence estimates valid also in the cases when the exact solution has a reduced regularity due to re-entering corners of the domain boundary. Numerical experiments confirm the theoretical results and show the potential of our proposed metho

Sum Rules and Ward Identities in the Kondo Lattice

We derive a generalized Luttinger-Ward expression for the Free energy of a many body system involving a constrained Hilbert space. In the large $N$ limit, we are able to explicity write the entropy as a functional of the Green's functions. Using this method we obtain a Luttinger sum rule for the Kondo lattice. One of the fascinating aspects of the sum rule, is that it contains two components, one describing the heavy electron Fermi surface, the other, a sea of oppositely charged, spinless fermions. In the heavy electron state, this sea of spinless fermions is completely filled and the electron Fermi surface expands by one electron per unit cell to compensate the positively charged background, forming a ``large'' Fermi surface. Arbitrarily weak magnetism causes the spinless Fermi sea to annihilate with part of the Fermi sea of the conduction electrons, leading to a small Fermi surface. Our results thus enable us to show that the Fermi surface volume contracts from a large, to a small volume at a quantum critical point. However, the sum rules also permit the possible formation of a new phase, sandwiched between the antiferromagnet and the heavy electron phase, where the charged spinless fermions develop a true Fermi surface.Comment: 24 pages, 4 figures. Version two contains a proof of the "Entropy formula" which connects the entropy directly to the Green's functions. Version three contains corrections to typos and a more extensive discussion of the physics at finite

NanoUPLC-MSE proteomic data assessment of soybean seeds using the Uniprot database.

Background: Recombinant DNA technology has been extensively employed to generate a variety of products from genetically modified organisms (GMOs) over the last decade, and the development of technologies capable of analyzing these products is crucial to understanding gene expression patterns. Liquid chromatography coupled with mass spectrometry is a powerful tool for analyzing protein contents and possible expression modifications in GMOs. Specifically, the NanoUPLC-MSE technique provides rapid protein analyses of complex mixtures with supported steps for high sample throughput, identification and quantization using low sample quantities with outstanding repeatability. Here, we present an assessment of the peptide and protein identification and quantification of soybean seed EMBRAPA BR16 cultivar contents using NanoUPLC-MSE and provide a comparison to the theoretical tryptic digestion of soybean sequences from Uniprot database. Results: The NanoUPLC-MSE peptide analysis resulted in 3,400 identified peptides, 58% of which were identified to have no miscleavages. The experiment revealed that 13% of the peptides underwent in-source fragmentation, and 82% of the peptides were identified with a mass measurement accuracy of less than 5 ppm. More than 75% of the identified proteins have at least 10 matched peptides, 88% of the identified proteins have greater than 30% of coverage, and 87% of the identified proteins occur in all four replicates. 78% of the identified proteins correspond to all glycinin and betaconglycinin chains. The theoretical Uniprot peptide database has 723,749 entries, and 548,336 peptides have molecular weights of greater than 500 Da. Seed proteins represent 0.86% of the protein database entries. At the peptide level, trypsin-digested seed proteins represent only 0.3% of the theoretical Uniprot peptide database. A total of 22% of all database peptides have a pI value of less than 5, and 25% of them have a pI value between 5 and 8. Based on the detection range of typical NanoUPLC-MSE experiments, i.e., 500 to 5000 Da, 64 proteins will not be identified. Conclusions: NanoUPLC-MSE experiments provide good protein coverage within a peptide error of 5 ppm and a wide MW detection range from 500 to 5000 Da. A second digestion enzyme should be used depending on the tissue or proteins to be analyzed. In the case of seed tissue, trypsin protein digestion results offer good databank coverage. The Uniprot database has many duplicate entries that may result in false protein homolog associations when using NanoUPLC-MSE analysis. The proteomic profile of the EMBRAPA BR-16 seed lacks certain described proteins relative to the profiles of transgenic soybeans reported in other works