Local Current Distribution and "Hot Spots" in the Integer Quantum Hall Regime

In a recent experiment, the local current distribution of a two-dimensional electron gas in the quantum Hall regime was probed by measuring the variation of the conductance due to local gating. The main experimental finding was the existence of "hot spots", i.e. regions with high degree of sensitivity to local gating, whose density increases as one approaches the quantum Hall transition. However, the direct connection between these "hot spots" and regions of high current flow is not clear. Here, based on a recent model for the quantum Hall transition consisting of a mixture of perfect and quantum links, the relation between the "hot spots" and the current distribution in the sample has been investigated. The model reproduces the observed dependence of the number and sizes of "hot spots" on the filling factor. It is further demonstrated that these "hot spots" are not located in regions where most of the current flows, but rather, in places where the currents flow both when injected from the left or from the right. A quantitative measure, the harmonic mean of these currents is introduced and correlates very well with the "hot spots" positions

Magic numbers in polymer phase separation -- the importance of being rigid

Cells possess non-membrane-bound bodies, many of which are now understood as phase-separated condensates. One class of such condensates is composed of two polymer species, where each consists of repeated binding sites that interact in a one-to-one fashion with the binding sites of the other polymer. Previous biologically-motivated modeling of such a two-component system surprisingly revealed that phase separation is suppressed for certain combinations of numbers of binding sites. This phenomenon, dubbed the "magic-number effect", occurs if the two polymers can form fully-bonded small oligomers by virtue of the number of binding sites in one polymer being an integer multiple of the number of binding sites of the other. Here we use lattice-model simulations and analytical calculations to show that this magic-number effect can be greatly enhanced if one of the polymer species has a rigid shape that allows for multiple distinct bonding conformations. Moreover, if one species is rigid, the effect is robust over a much greater range of relative concentrations of the two species. Our findings advance our understanding of the fundamental physics of two-component polymer-based phase-separation and suggest implications for biological and synthetic systems.Comment: 8 pages + 15 pages S

A New Spin-Orbit Induced Universality Class in the Quantum Hall Regime ?

Using heuristic arguments and numerical simulations it is argued that the critical exponent $\nu$ describing the localization length divergence at the quantum Hall transition is modified in the presence of spin-orbit scattering with short range correlations. The exponent is very close to $\nu=4/3$, the percolation correlation length exponent, the prediction of a semi-classical argument. In addition, a region of weakly localized regime, where the localization length is exponentially large, is conjectured.Comment: 4 two-column pages including 4 eps figure

Revealing Cosmic Rotation

Cosmological Birefringence (CB), a rotation of the polarization plane of radiation coming to us from distant astrophysical sources, may reveal parity violation in either the electromagnetic or gravitational sectors of the fundamental interactions in nature. Until only recently this phenomenon could be probed with only radio observations or observations at UV wavelengths. Recently, there is a substantial effort to constrain such non-standard models using observations of the rotation of the polarization plane of cosmic microwave background (CMB) radiation. This can be done via measurements of the $B$-modes of the CMB or by measuring its TB and EB correlations which vanish in the standard model. In this paper we show that $EB$ correlations-based estimator is the best for upcoming polarization experiments. The $EB$ based estimator surpasses other estimators because it has the smallest noise and of all the estimators is least affected by systematics. Current polarimeters are optimized for the detection of $B$-mode polarization from either primordial gravitational waves or by large scale structure via gravitational lensing. In the paper we also study optimization of CMB experiments for the detection of cosmological birefringence, in the presence of instrumental systematics, which by themselves are capable of producing $EB$ correlations; potentially mimicking CB.Comment: 10 pages, 3 figures, 2 table

Structure and transport in multi-orbital Kondo systems

We consider Kondo impurity systems with multiple local orbitals, such as rare earth ions in a metallic host or multi--level quantum dots coupled to metallic leads. It is shown that the multiplet structure of the local orbitals leads to multiple Kondo peaks above the Fermi energy $E_F$, and to ``shadow'' peaks below $E_F$. We use a slave boson mean field theory, which recovers the strong coupling Fermi liquid fixed point, to calculate the Kondo peak positions, widths, and heights analytically at T=0, and NCA calculations to fit the temperature dependence of high--resolution photoemission spectra of Ce compounds. In addition, an approximate conductance quantization for transport through multi--level quantum dots or single--atom transistors in the Kondo regime due to a generalized Friedel sum rule is demonstrated.Comment: 4 pages, 3 figures. Invited article, 23rd International Conference on Low Temperature Physics LT23, Hiroshima, Japan 200

Shot Noise through a Quantum Dot in the Kondo Regime

The shot noise in the current through a quantum dot is calculated as a function of voltage from the high-voltage, Coulomb blockaded regime to the low-voltage, Kondo regime. Using several complementary approaches, it is shown that the zero-frequency shot noise (scaled by the voltage) exhibits a non-monotonic dependence on voltage, with a peak around the Kondo temperature. Beyond giving a good estimate of the Kondo temperature, it is shown that the shot noise yields additional information on the effects of electronic correlations on the local density of states in the Kondo regime, unaccessible in traditional transport measurements.Comment: 4 pages, 1 figur

Electron correlation resonances in the transport through a single quantum level

Correlation effects in the transport properties of a single quantum level coupled to electron reservoirs are discussed theoretically using a non-equilibrium Green functions approach. Our method is based on the introduction of a second-order self-energy associated with the Coulomb interaction that consistently eliminates the pathologies found in previous perturbative calculations. We present results for the current-voltage characteristic illustrating the different correlation effects that may be found in this system, including the Kondo anomaly and Coulomb blockade. We finally discuss the experimental conditions for the simultaneous observation of these effects in an ultrasmall quantum dot.Comment: 4 pages (two columns), 3 figures under reques

The effect of the spin-orbit geometric phase on the spectrum of Aharonov-Bohm oscillations in a semiconductor mesoscopic ring

Taking into account the spin precession caused by the spin-orbit splitting of the conduction band in semiconductor quantum wells, we have calculated the Fourier spectra of conductance and state-density correlators in a 2D ring, in order to investigate the structure of the main peak corresponding to Aharonov-Bohm oscillations. In narrow rings the peak structure is determined by the competition between the spin-orbit and the Zeeman couplings. The latter leads to a peak broadening, and produces the peak splitting in the state-density Fourier spectrum. We have found an oscillation of the peak intensity as a function of the spin-orbit coupling constant, and this effect of the quantum interference caused by the spin geometric phase is destroyed with increasing Zeeman coupling.Comment: 4 pages, 3 figures, uses epsfig.st

Computing Stable Coalitions: Approximation Algorithms for Reward Sharing

Consider a setting where selfish agents are to be assigned to coalitions or projects from a fixed set P. Each project k is characterized by a valuation function; v_k(S) is the value generated by a set S of agents working on project k. We study the following classic problem in this setting: "how should the agents divide the value that they collectively create?". One traditional approach in cooperative game theory is to study core stability with the implicit assumption that there are infinite copies of one project, and agents can partition themselves into any number of coalitions. In contrast, we consider a model with a finite number of non-identical projects; this makes computing both high-welfare solutions and core payments highly non-trivial. The main contribution of this paper is a black-box mechanism that reduces the problem of computing a near-optimal core stable solution to the purely algorithmic problem of welfare maximization; we apply this to compute an approximately core stable solution that extracts one-fourth of the optimal social welfare for the class of subadditive valuations. We also show much stronger results for several popular sub-classes: anonymous, fractionally subadditive, and submodular valuations, as well as provide new approximation algorithms for welfare maximization with anonymous functions. Finally, we establish a connection between our setting and the well-studied simultaneous auctions with item bidding; we adapt our results to compute approximate pure Nash equilibria for these auctions.Comment: Under Revie

Transmission Phase Shift of a Quantum Dot with Kondo Correlations

We study the effects of Kondo correlations on the transmission phase shift of a quantum dot in an Aharonov-Bohm ring. We predict in detail how the development of a Kondo resonance should affect the dependence of the phase shift on transport voltage, gate voltage and temperature. This system should allow the first direct observation of the well-known scattering phase shift of pi/2 expected (but not directly measurable in bulk systems) at zero temperature for an electron scattering off a spin-1/2 impurity that is screened into a singlet.Comment: 4 pages Revtex, 4 figures, final published versio