Exchange Coupling in a One-Dimensional Wigner Crystal

We consider a long quantum wire at low electron densities. In this strong interaction regime a Wigner crystal may form, in which electrons comprise an antiferromagnetic Heisenberg spin chain. The coupling constant J is exponentially small, as it originates from tunneling of two neighboring electrons through the segregating potential barrier. We study this exponential dependence, properly accounting for the many-body effects and the finite width of the wire.Comment: 4 pages, 3 figure

Impurity effects in few-electron quantum dots: Incipient Wigner molecule regime

Numerically exact path-integral Monte Carlo data are presented for $N\leq 10$ strongly interacting electrons confined in a 2D parabolic quantum dot, including a defect to break rotational symmetry. Low densities are studied, where an incipient Wigner molecule forms. A single impurity is found to cause drastic effects: (1) The standard shell-filling sequence with magic numbers $N=4,6,9$, corresponding to peaks in the addition energy $\Delta(N)$, is destroyed, with a new peak at N=8, (2) spin gaps decrease, (3) for N=8, sub-Hund's rule spin S=0 is induced, and (4) spatial ordering of the electrons becomes rather sensitive to spin. We also comment on the recently observed bunching phenomenon.Comment: 7 pages, 1 table, 4 figures, accepted for publication in Europhysics Letter

Überprüfung der Bezugskurven der Schweizer Version des Freiburger Zahlen- und Einsilbertests

Zusammenfassung: Hintergrund: Die Schweizer Ausgabe des Freiburger Sprachverständlichkeitstests unterscheidet sich von der deutschen Version u.a. durch den Ersatz von 5 in der Schweiz ungebräuchlichen einsilbigen Testworten. Zudem wird keine Freifeldentzerrung benutzt und die die sich aus dem Freifeldübertragungsmaß ergebende Differenz von 6dB zwischen Lautsprecher und Kopfhörer wird bei der Kalibrierung nicht berücksichtigt. Der vor einiger Zeit eingeführte Pegelausgleich zwischen den Prüfworten und Anpassungen in der Kalibrierung veranlassten uns zur Überprüfung der Bezugskurven. Patienten/Methoden: Bei 20 normal hörenden Versuchpersonen wurde das Sprachverstehen von Zahlen und einsilbigen Wörtern mit Kopfhörern und Lautsprechern geprüft. Ergebnisse: Der Pegel für 50% Sprachverstehen lag bei Lautsprecherdarbietung im Mittel um 7,5dB niedriger ist als bei Kopfhörerdarbietung. Die mittlere Pegeldifferenz zwischen Zahlen und Einsilbern betrug 9,6dB, liegt also deutlich unter den 14dB der heute in der Schweiz empfohlenen Bezugskurven. Fazit: Die heute in der Schweiz empfohlenen Bezugskurven stimmen für Einsilber bei Kopfhörerdarbietung gut mit unseren Messungen überein, nicht aber für Zahlen und bei Lautsprecherdarbietun

Exchange interaction in quantum rings and wires in the Wigner-crystal limit

We present a controlled method for computing the exchange coupling in correlated one-dimensional electron systems based on the relation between the exchange constant and the pair-correlation function of spinless electrons. This relation is valid in several independent asymptotic regimes, including low electron density case, under the general condition of a strong spin-charge separation. Explicit formulas for the exchange constant are obtained for thin quantum rings and wires with realistic Coulomb interactions by calculating the pair-correlation function via a many-body instanton approach. A remarkably smooth interpolation between high and low electron density results is shown to be possible. These results are applicable to the case of one-dimensional wires of intermediate width as well. Our method can be easily generalized to other interaction laws, such as the inverse distance squared one of the Calogero-Sutherland-Moser model. We demonstrate excellent agreement with the known exact results for the latter model and show that they are relevant for a realistic experimental setup in which the bare Coulomb interaction is screened by an edge of a two-dimensional electron gas.Comment: 12 pages, 5 figure

Conductance quantization and snake states in graphene magnetic waveguides

We consider electron waveguides (quantum wires) in graphene created by suitable inhomogeneous magnetic fields. The properties of uni-directional snake states are discussed. For a certain magnetic field profile, two spatially separated counter-propagating snake states are formed, leading to conductance quantization insensitive to backscattering by impurities or irregularities of the magnetic field.Comment: 5 pages, 4 figures, final version accepted as Rapid Comm. in PR

Effective charge-spin models for quantum dots

It is shown that at low densities, quantum dots with few electrons may be mapped onto effective charge-spin models for the low-energy eigenstates. This is justified by defining a lattice model based on a many-electron pocket-state basis in which electrons are localised near their classical ground-state positions. The equivalence to a single-band Hubbard model is then established leading to a charge-spin ($t-J-V$) model which for most geometries reduces to a spin (Heisenberg) model. The method is refined to include processes which involve cyclic rotations of a ``ring'' of neighboring electrons. This is achieved by introducing intermediate lattice points and the importance of ring processes relative to pair-exchange processes is investigated using high-order degenerate perturbation theory and the WKB approximation. The energy spectra are computed from the effective models for specific cases and compared with exact results and other approximation methods.Comment: RevTex, 24 pages, 7 figures submitted as compressed and PostScript file

Proximity-induced superconductivity in Landau-quantized graphene monolayers

We consider massless Dirac fermions in a graphene monolayer in the ballistic limit, subject to both a perpendicular magnetic field B and a proximity-induced pairing gap Δ. When the chemical potential is at the Dirac point, our exact solution of the Bogoliubov–de Gennes equation yields Δ-independent relativistic Landau levels. Since eigenstates depend on Δ, many observables nevertheless are sensitive to pairing, e.g., the local density of states or the edge state spectrum. By solving the problem with an additional in-plane electric field, we also discuss how snake states are influenced by a pairing gap

Spin and Charge Luttinger-Liquid Parameters of the One-Dimensional Electron Gas

Low-energy properties of the homogeneous electron gas in one dimension are completely described by the group velocities of its charge (plasmon) and spin collective excitations. Because of the long range of the electron-electron interaction, the plasmon velocity is dominated by an electrostatic contribution and can be estimated accurately. In this Letter we report on Quantum Monte Carlo simulations which demonstrate that the spin velocity is substantially decreased by interactions in semiconductor quantum wire realizations of the one-dimensional electron liquid.Comment: 13 pages, figures include

Cogan's syndrome: clinical evolution of deafness and vertigo in three patients

The aim of this study was to evaluate the clinical symptoms, the otoneurological examinations, the treatment and the clinical course of three patients suffering from Cogan's syndrome, a rare disease based on the clinical association of a non-syphilitic interstitial keratitis with a cochleo-vestibular deficit. This case series involved three patients with follow up. The clinical course of the three patients (aged 30, 48 and 49years) with Cogan's syndrome during a follow-up period of 2 to 6years is reported. All patients underwent complete otoneurological, ophthalmologic and rheumatologic examinations and were treated with immunosuppressive therapy such as glucocorticoids and cyclophosphamide in two and glucocorticoids and methotrexate in one patient. Using immunosuppressive therapy, ophthalmologic symptoms disappeared rapidly in two patients. Hearing improved only in one and stabilized in a second patient. One patient died after 6years of treatment because of complications of generalized vasculitis. Early diagnosis and rapid initiation of a combined immunosuppressive therapy such as corticosteroids and cyclophosphamide seem to be important in controlling the disease and avoiding persistent deafness. Whether systemic complications and a fatal outcome also can be prevented is still questionabl