A Single Impurity in Tomonaga-Luttinger Liquids

The problem of a single impurity in one dimensional Tomonaga-Luttinger liquids with a repulsive electron-electron interaction is discussed. We find that the renormalization group flow diagram for the parameters characterizing the impurity is rather complex. Apart from the fixed points corresponding to two weakly connected semi-infinite wires, the flow diagram contains additional fixed points which control the low temperature physics when the bare potential of the impurity is not strong.Comment: To be published in the Philosophical Magazine in the Proceedings of the "MINERVA WORKSHOP on MESOSCOPICS, FRACTALS and NEURAL NETWORKS", Eilat, Israel, March 199

Significant g-factor values of a two-electron ground state in quantum dots with spin-orbit coupling

The magnetization of semiconductor quantum dots in the presence of spin-orbit coupling and interactions is investigated numerically. When the dot is occupied by two electrons we find that a level crossing between the two lowest many-body eigenstates may occur as a function of the spin-orbit coupling strength. This level crossing is accompanied by a non-vanishing magnetization of the ground-state. Using first order perturbation theory as well as exact numerical diagonalization of small clusters we show that the tendency of interactions to cause Stoner-like instability is enhanced by the SO coupling. The resulting g-factor can have a significant value, and thus may influence g-factor measurements. Finally we propose an experimental method by which the predicted phenomenon can be observed.Comment: 7+ pages, 7 figure

Superconductor-to-Metal Transitions in Dissipative Chains of Mesoscopic Grains and Nanowires

The interplay of quantum fluctuations and dissipation in chains of mesoscopic superconducting grains is analyzed, and the results are also applied to nanowires. It is shown that in 1-d arrays of resistively shunted Josephson junctions, the superconducting-normal charge relaxation within the grains plays an important role. At zero temperature, two superconducting phases can exist, depending primarily on the strength of the dissipation. In the fully superconducting phase (FSC), each grain acts superconducting, and the coupling to the dissipative conduction is important. In the SC* phase, the dissipation is irrelevant at long wavelengths. The phase transitions between these two superconducting phases and the normal metallic phase may be either local or global, and possess rich and complex critical properties. These are inferred from both weak and strong coupling renormalization group analyses. At intermediate temperatures, near either superconductor-to-normal phase transition, there are regimes of super-metallic behavior, in which the resistivity first decreases gradually with decreasing temperature before eventually increasing as temperature is lowered further. The results on chains of Josephson junctions are extended to continuous superconducting nanowires and the subtle issue of whether these can exhibit an FSC phase is considered. Potential relevance to superconductor-metal transitions in other systems is also discussed.Comment: 42 pages, 14 figure

A Joint Data Compression and Time-Delay Estimation Method For Distributed Systems via Extremum Encoding

Motivated by the proliferation of mobile devices, we consider a basic form of the ubiquitous problem of time-delay estimation (TDE), but with communication constraints between two non co-located sensors. In this setting, when joint processing of the received signals is not possible, a compression technique that is tailored to TDE is desirable. For our basic TDE formulation, we develop such a joint compression-estimation strategy based on the notion of what we term "extremum encoding", whereby we send the index of the maximum of a finite-length time-series from one sensor to another. Subsequent joint processing of the encoded message with locally observed data gives rise to our proposed time-delay "maximum-index"-based estimator. We derive an exponentially tight upper bound on its error probability, establishing its consistency with respect to the number of transmitted bits. We further validate our analysis via simulations, and comment on potential extensions and generalizations of the basic methodology

Dynamical Effective Medium Theory for Quantum Spins and Multipoles

A dynamical effective medium theory is presented for quantum spins and higher multipoles such as quadrupole moments. The theory is a generalization of the spherical model approximation for the Ising model, and is accurate up to O(1/z_n) where z_n is the number of interacting neighbors. The polarization function is optimized under the condition that it be diagonal in site indices. With use of auxiliary fields and path integrals, the theory is flexibly applied to quantum spins and higher multipoles with many interacting neighbors. A Kondo-type screening of each spin is proposed for systems with extreme quantum fluctuations but without conduction electrons.Comment: 16 pages, 3 Postscript figure

Formation of Super-Earths

Super-Earths are the most abundant planets known to date and are characterized by having sizes between that of Earth and Neptune, typical orbital periods of less than 100 days and gaseous envelopes that are often massive enough to significantly contribute to the planet's overall radius. Furthermore, super-Earths regularly appear in tightly-packed multiple-planet systems, but resonant configurations in such systems are rare. This chapters summarizes current super-Earth formation theories. It starts from the formation of rocky cores and subsequent accretion of gaseous envelopes. We follow the thermal evolution of newly formed super-Earths and discuss their atmospheric mass loss due to disk dispersal, photoevaporation, core-cooling and collisions. We conclude with a comparison of observations and theoretical predictions, highlighting that even super-Earths that appear as barren rocky cores today likely formed with primordial hydrogen and helium envelopes and discuss some paths forward for the future.Comment: Invited review accepted for publication in the 'Handbook of Exoplanets,' Planet Formation section, Springer Reference Works, Juan Antonio Belmonte and Hans Deeg, Ed