Raviart Thomas Petrov-Galerkin Finite Elements

The general theory of Babu\v{s}ka ensures necessary and sufficient conditions for a mixed problem in classical or Petrov-Galerkin form to be well posed in the sense of Hadamard. Moreover, the mixed method of Raviart-Thomas with low-level elements can be interpreted as a finite volume method with a non-local gradient. In this contribution, we propose a variant of type Petrov-Galerkin to ensure a local computation of the gradient at the interfaces of the elements. The in-depth study of stability leads to a specific choice of the test functions. With this choice, we show on the one hand that the mixed Petrov-Galerkin obtained is identical to the finite volumes scheme "volumes finis \`a 4 points" ("VF4") of Faille, Gallo\"uet and Herbin and to the condensation of mass approach developed by Baranger, Maitre and Oudin. On the other hand, we show the stability via an inf-sup condition and finally the convergence with the usual methods of mixed finite elements.Comment: arXiv admin note: text overlap with arXiv:1710.0439

Chaos and Interacting Electrons in Ballistic Quantum Dots

We show that the classical dynamics of independent particles can determine the quantum properties of interacting electrons in the ballistic regime. This connection is established using diagrammatic perturbation theory and semiclassical finite-temperature Green functions. Specifically, the orbital magnetism is greatly enhanced over the Landau susceptibility by the combined effects of interactions and finite size. The presence of families of periodic orbits in regular systems makes their susceptibility parametrically larger than that of chaotic systems, a difference which emerges from correlation terms.Comment: 4 pages, revtex, includes 3 postscript fig

Semiclassical Approach to Orbital Magnetism of Interacting Diffusive Quantum Systems

We study interaction effects on the orbital magnetism of diffusive mesoscopic quantum systems. By combining many-body perturbation theory with semiclassical techniques, we show that the interaction contribution to the ensemble averaged quantum thermodynamic potential can be reduced to an essentially classical operator. We compute the magnetic response of disordered rings and dots for diffusive classical dynamics. Our semiclassical approach reproduces the results of previous diagrammatic quantum calculations.Comment: 8 pages, revtex, includes 1 postscript fi

Reflection Symmetric Ballistic Microstructures: Quantum Transport Properties

We show that reflection symmetry has a strong influence on quantum transport properties. Using a random S-matrix theory approach, we derive the weak-localization correction, the magnitude of the conductance fluctuations, and the distribution of the conductance for three classes of reflection symmetry relevant for experimental ballistic microstructures. The S-matrix ensembles used fall within the general classification scheme introduced by Dyson, but because the conductance couples blocks of the S-matrix of different parity, the resulting conductance properties are highly non-trivial.Comment: 4 pages, includes 3 postscript figs, uses revte

Spin and Conductance-Peak-Spacing Distributions in Large Quantum Dots: A Density Functional Theory Study

We use spin-density-functional theory to study the spacing between conductance peaks and the ground-state spin of 2D model quantum dots with up to 200 electrons. Distributions for different ranges of electron number are obtained in both symmetric and asymmetric potentials. The even/odd effect is pronounced for small symmetric dots but vanishes for large asymmetric ones, suggesting substantially stronger interaction effects than expected. The fraction of high-spin ground states is remarkably large.Comment: 4 pages, 3 figure

Statistics of Wave Functions in Disordered Systems with Applications to Coulomb Blockade Peak Spacing

Despite considerable work on the energy-level and wavefunction statistics of disordered quantum systems, numerical studies of those statistics relevant for electron-electron interactions in mesoscopic systems have been lacking. We plug this gap by using a tight-binding model to study a wide variety of statistics for the two-dimensional, disordered quantum system in the diffusive regime. Our results are in good agreement with random matrix theory (or its extensions) for simple statistics such as the probability distribution of energy levels or spatial correlation of a wavefunction. However, we see substantial disagreement in several statistics which involve both integrating over space and different energy levels, indicating that disordered systems are more complex than previously thought. These are exactly the quantities relevant to electron-electron interaction effects in quantum dots; in fact, we apply these results to the Coulomb blockade, where we find altered spacings between conductance peaks and wider spin distributions than traditionally expected.Comment: Accepted for publication in Phys Rev

On the Sign Problem in the Hirsch-Fye Algorithm for Impurity Problems

We show that there is no fermion sign problem in the Hirsch and Fye algorithm for the single-impurity Anderson model. Beyond the particle-hole symmetric case for which a simple proof exists, this has been known only empirically. Here we prove the nonexistence of a sign problem for the general case by showing that each spin trace for a given Ising configuration is separately positive. We further use this insight to analyze under what conditions orbitally degenerate Anderson models or the two-impurity Anderson model develop a sign.Comment: 2 pages, no figure; published versio

Quantum Electrodynamics of the Helium Atom

Using singlet S states of the helium atom as an example, I describe precise calculation of energy levels in few-electron atoms. In particular, a complete set of effective operators is derived which generates O(m*alpha^6) relativistic and radiative corrections to the Schr"odinger energy. Average values of these operators can be calculated using a variational Schr"odinger wave function.Comment: 23 pages, revte

The Thermopower of Quantum Chaos

The thermovoltage of a chaotic quantum dot is measured using a current heating technique. The fluctuations in the thermopower as a function of magnetic field and dot shape display a non-Gaussian distribution, in agreement with simulations using Random Matrix Theory. We observe no contributions from weak localization or short trajectories in the thermopower.Comment: 4 pages, 3 figures, corrected: accidently omitted author in the Authors list, here (not in the article

Characterization of one-dimensional quantum channels in InAs/AlSb

We report the magnetoresistance characteristics of one-dimensional electrons confined in a single InAs quantum well sandwiched between AlSb barriers. As a result of a novel nanofabrication scheme that utilizes a 3nm-shallow wet chemical etching to define the electrostatic lateral confinement, the system is found to possess three important properties: specular boundary scattering, a strong lateral confinement potential, and a conducting channel width that is approximately the lithography width. Ballistic transport phenomena, including the quenching of the Hall resistance, the last Hall plateau, and a strong negative bend resistance, are observed at 4K in cross junctions with sharp corners. In a ring geometry, we have observed Aharonov-Bohm interference that exhibits characteristics different from those of the GaAs counterpart due to the ballistic nature of electron transport and the narrowness of the conducting channel width.Comment: pdf-file, 8 figures, to be published in Phys. Rev.