Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity

We consider positive solutions $u$ of the semilinear biharmonic equation $\Delta^2 u = |x|^{-\frac{n+4}{2}} g(|x|^\frac{n-4}{2} u)$ in $\mathbb R^n \setminus \{0\}$ with non-removable singularities at the origin. Under natural assumptions on the nonlinearity $g$, we show that $|x|^\frac{n-4}{2} u$ is a periodic function of $\ln |x|$ and we classify all such solutions.Comment: To V. Maz'ya on the occasion of his 80th birthday; references adde

Tunable dynamical channel blockade in double-dot Aharonov-Bohm interferometers

We study electronic transport through an Aharonov-Bohm interferometer with single-level quantum dots embedded in the two arms. The full counting statistics in the shot-noise regime is calculated to first order in the tunnel-coupling strength. The interplay of interference and charging energy in the dots leads to a dynamical channel blockade that is tunable by the magnetic flux penetrating the Aharonov-Bohm ring. We find super-Poissonian behavior with diverging second and higher cumulants when the Aharonov-Bohm flux approaches an integer multiple of the flux quantum.Comment: published version, 10 pages, 10 figure

Tunneling resonances in quantum dots: Coulomb interaction modifies the width

Single-electron tunneling through a zero-dimensional state in an asymmetric double-barrier resonant-tunneling structure is studied. The broadening of steps in the $I$--$V$ characteristics is found to strongly depend on the polarity of the applied bias voltage. Based on a qualitative picture for the finite-life-time broadening of the quantum dot states and a quantitative comparison of the experimental data with a non-equilibrium transport theory, we identify this polarity dependence as a clear signature of Coulomb interaction.Comment: 4 pages, 4 figure

Influence of spin waves on transport through a quantum-dot spin valve

We study the influence of spin waves on transport through a single-level quantum dot weakly coupled to ferromagnetic electrodes with noncollinear magnetizations. Side peaks appear in the differential conductance due to emission and absorption of spin waves. We, furthermore, investigate the nonequilibrium magnon distributions generated in the source and drain lead. In addition, we show how magnon-assisted tunneling can generate a fullly spin-polarized current without an applied transport voltage. We discuss the influence of spin waves on the current noise. Finally, we show how the magnonic contributions to the exchange field can be detected in the finite-frequency Fano factor.Comment: published version, 15 pages, 10 figure

Full Counting Statistics in Strongly Interacting Systems: Non-Markovian Effects

We present a theory of full counting statistics for electron transport through interacting electron systems with non-Markovian dynamics. We illustrate our approach for transport through a single-level quantum dot and a metallic single-electron transistor to second order in the tunnel-coupling strength, and discuss under which circumstances non-Markovian effects appear in the transport properties.Comment: 4 pages, 2 figures, LaTeX; typos added, references adde

Hanle Effect in Transport through Quantum Dots Coupled to Ferromagnetic Leads

We suggest a series of transport experiments on spin precession in quantum dots coupled to one or two ferromagnetic leads. Dot spin states are created by spin injection and analyzed via the linear conductance through the dot, while an applied magnetic field gives rise to the Hanle effect. Such a Hanle experiment can be used to determine the spin lifetime in the quantum dot, to measure the spin injection efficiency into the dot, as well as proving the existence of intrinsic spin precession which is driven by the Coulomb interaction.Comment: 7 pages, 4 figures, minor changes, added reference

Resonant Tunneling through Multi-Level and Double Quantum Dots

We study resonant tunneling through quantum-dot systems in the presence of strong Coulomb repulsion and coupling to the metallic leads. Motivated by recent experiments we concentrate on (i) a single dot with two energy levels and (ii) a double dot with one level in each dot. Each level is twofold spin-degenerate. Depending on the level spacing these systems are physical realizations of different Kondo-type models. Using a real-time diagrammatic formulation we evaluate the spectral density and the non-linear conductance. The latter shows a novel triple-peak resonant structure.Comment: 4 pages, ReVTeX, 4 Postscript figure

Exploring the Relationship of Relative Telomere Length and the Epigenetic Clock in the LipidCardio Cohort

Telomere length has been accepted widely as a biomarker of aging. Recently, a novel candidate biomarker has been suggested to predict an individual’s chronological age with high accuracy: The epigenetic clock is based on the weighted DNA methylation (DNAm) fraction of a number of cytosine-phosphate-guanine sites (CpGs) selected by penalized regression analysis. Here, an established methylation-sensitive single nucleotide primer extension method was adapted, to estimate the epigenetic age of the 1005 participants of the LipidCardio Study, a patient cohort characterised by high prevalence of cardiovascular disease, based on a seven CpGs epigenetic clock. Furthermore, we measured relative leukocyte telomere length (rLTL) to assess the relationship between the established and the promising new measure of biological age. Both rLTL (0.79 ± 0.14) and DNAm age (69.67 ± 7.27 years) were available for 773 subjects (31.6% female; mean chronological age= 69.68 ± 11.01 years; mean DNAm age acceleration = −0.01 ± 7.83 years). While we detected a significant correlation between chronological age and DNAm age (n = 779, R = 0.69), we found neither evidence of an association between rLTL and the DNAm age (β = 3.00, p = 0.18) nor rLTL and the DNAm age acceleration (β = 2.76, p = 0.22) in the studied cohort, suggesting that DNAm age and rLTL measure different aspects of biological age

Quantum tunneling through planar p-n junctions in HgTe quantum wells

We demonstrate that a p-n junction created electrically in HgTe quantum wells with inverted band-structure exhibits interesting intraband and interband tunneling processes. We find a perfect intraband transmission for electrons injected perpendicularly to the interface of the p-n junction. The opacity and transparency of electrons through the p-n junction can be tuned by changing the incidence angle, the Fermi energy and the strength of the Rashba spin-orbit interaction. The occurrence of a conductance plateau due to the formation of topological edge states in a quasi-one-dimensional p-n junction can be switched on and off by tuning the gate voltage. The spin orientation can be substantially rotated when the samples exhibit a moderately strong Rashba spin-orbit interaction.Comment: 4 pages, 4 figure