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We study the temperature flow of conductivities in a gated GaAs two-dimensional electron gas (2DEG) containing self-assembled InAs dots and compare the results with recent theoretical predictions. By changing the gate voltage, we are able to tune the 2DEG density and thus vary disorder and spin-splitting. Data for both the spin-resolved and spin-degenerate phase transitions are presented, the former collapsing to the latter with decreasing gate voltage and/or decreasing spin-splitting. The experimental results support a recent theory, based on modular symmetry, which predicts how the critical Hall conductivity varies with spin-splitting., Comment: 22 pages

There is considerable experimental evidence for the existence in Quantum Hall systems of an approximate emergent discrete symmetry, $\Gamma_0(2) \subset SL(2,Z)$. The evidence consists of the robustness of the tests of a suite a predictions concerning the transitions between the phases of the system as magnetic fields and temperatures are varied, which follow from the existence of the symmetry alone. These include the universality of and quantum numbers of the fixed points which occur in these transitions; selection rules governing which phases may be related by transitions; and the semi-circular trajectories in the Ohmic-Hall conductivity plane which are followed during the transitions. We explore the implications of this symmetry for Quantum Hall systems involving {\it two} charge-carrying fluids, and so obtain predictions both for bilayer systems and for single-layer systems for which the Landau levels have a spin degeneracy. We obtain similarly striking predictions which include the novel new phases which are seen in these systems, as well as a prediction for semicircle trajectories which are traversed by specific combinations of the bilayer conductivities as magnetic fields are varied at low temperatures., Comment: 12 pages, 8 figures; discussion of magnetic field dependence modified and figures and references updated in v2

Low-energy transport measurements in Quantum Hall systems have been argued to be governed by emergent modular symmetries whose predictions are robust against many of the detailed microscopic dynamics. We propose the recently-observed quantum Hall effect in graphene as a test of these ideas, and identify to this end a class of predictions for graphene which would follow from the same modular arguments. We are led to a suite of predictions for high mobility samples that differs from those obtained for the conventional quantum Hall effect in semiconductors, including: predictions for the locations of the quantum Hall plateaux; predictions for the positions of critical points on transitions between plateaux; a selection rule for which plateaux can be connected by low-temperature transitions; and a semi-circle law for conductivities traversed during these transitions. Many of these predictions appear to provide a good description of graphene measurements performed with intermediate-strength magnetic fields., Comment: 4 pages, 2 figures

We search for all Poisson brackets for the BTZ black hole which are consistent with the geometry of the commutative solution and are of lowest order in the embedding coordinates. For arbitrary values for the angular momentum we obtain two two-parameter families of contact structures. We obtain the symplectic leaves, which characterize the irreducible representations of the noncommutative theory. The requirement that they be invariant under the action of the isometry group restricts to $R\times S^1$ symplectic leaves, where $R$ is associated with the Schwarzschild time. Quantization may then lead to a discrete spectrum for the time operator., Comment: 10 pages

In various statistical-mechanical models the introduction of a metric onto the space of parameters (e.g. the temperature variable, $\beta$, and the external field variable, $h$, in the case of spin models) gives an alternative perspective on the phase structure. For the one-dimensional Ising model the scalar curvature, ${\cal R}$, of this metric can be calculated explicitly in the thermodynamic limit and is found to be ${\cal R} = 1 + \cosh (h) / \sqrt{\sinh^2 (h) + \exp (- 4 \beta)}$. This is positive definite and, for physical fields and temperatures, diverges only at the zero-temperature, zero-field ``critical point'' of the model. In this note we calculate ${\cal R}$ for the one-dimensional $q$-state Potts model, finding an expression of the form ${\cal R} = A(q,\beta,h) + B (q,\beta,h)/\sqrt{\eta(q,\beta,h)}$, where $\eta(q,\beta,h)$ is the Potts analogue of $\sinh^2 (h) + \exp (- 4 \beta)$. This is no longer positive definite, but once again it diverges only at the critical point in the space of real parameters. We remark, however, that a naive analytic continuation to complex field reveals a further divergence in the Ising and Potts curvatures at the Lee-Yang edge., Comment: 9 pages + 4 eps figures

We derive the implications of particle-vortex duality for the electromagnetic response of Quantum Hall systems beyond the linear-response regime. This provides a first theoretical explanation of the remarkable duality which has been observed in the nonlinear regime for the electromagnetic response of Quantum Hall systems., Comment: 7 pages, 1 figure, typeset in LaTeX

Biskup et al. [Phys. Rev. Lett. 84 (2000) 4794] have recently suggested that the loci of partition function zeroes can profitably be regarded as phase boundaries in the complex temperature or field planes. We obtain the Fisher zeroes for Ising and Potts models on non-planar (``thin'') regular random graphs using this approach, and note that the locus of Fisher zeroes on a Bethe lattice is identical to the corresponding random graph. Since the number of states appears as a parameter in the Potts solution the limiting locus of chromatic zeroes is also accessible., Comment: 10 pages, 4 figures

We show how particle-vortex duality implies the existence of a large non-abelian discrete symmetry group which relates the electromagnetic response for dual two-dimensional systems in a magnetic field. For conductors with charge carriers satisfying Fermi statistics (or those related to fermions by the action of the group), the resulting group is known to imply many, if not all, of the remarkable features of Quantum Hall systems. For conductors with boson charge carriers (modulo group transformations) a different group is predicted, implying equally striking implications for the conductivities of these systems, including a super-universality of the critical exponents for conductor/insulator and superconductor/insulator transitions in two dimensions and a hierarchical structure, analogous to that of the quantum Hall effect but different in its details. Our derivation shows how this symmetry emerges at low energies, depending only weakly on the details of dynamics of the underlying systems., Comment: 22 pages, LaTeX, 2 figures, uses revtex

It is known that the (exact) renormalization transformations for the one-dimensional Ising model in field can be cast in the form of a logistic map f(x) = 4 x (1 - x) with x a function of the Ising couplings. Remarkably, the line bounding the region of chaotic behaviour in x is precisely that defining the Yang-Lee edge singularity in the Ising model. In this paper we show that the one dimensional q-state Potts model for q greater than or equal to 1 also displays such behaviour. A suitable combination of Potts couplings can again be used to define an x satisfying f(x) = 4 x (1 -x). The Yang-Lee zeroes no longer lie on the unit circle in the complex z = exp (h) plane, but their locus is still reproduced by the boundary of the chaotic region in the logistic map., Comment: 6 pages, no figures

It is demonstrated that decimation of the one dimensional Ising model, with periodic boundary conditions, results in a non-linear renormalisation transformation for the couplings which can lead to chaotic behaviour when the couplings are complex. The recursion relation for the couplings under decimation is equivalent to the logistic map, or more generally the Mandelbrot map. In particular an imaginary external magnetic field can give chaotic trajectories in the space of couplings. The magnitude of the field must be greater than a minimum value which tends to zero as the critical point T=0 is approached, leading to a gap equation and associated critical exponent which are identical to those of the Lee-Yang edge singularity in one dimension., Comment: 8 pages, 2 figures, PlainTeX, corrected some typos

The Space Debris Sensor (SDS) is a NASA Class 1E technology demonstration external payload aboard the International Space Station (ISS). With approximately one square meter of detection area, the SDS is attached to the European Space Agency Columbus module facing the ISS velocity vector with minimal obstruction from ISS hardware. The SDS is the first flight demonstration of the Debris Resistive/Acoustic Grid Orbital NASA-Navy Sensor (DRAGONS) technology developed and matured over 10 years by the NASA Orbital Debris Program Office (ODPO), in concert with the DRAGONS consortium, to provide information on the sub-millimeter scale orbital debris environment. The SDS demonstrated the capacity to read 4 resistive grids at 1 Hz, 40 acoustic sensors at 500 kHz, and record and downlink impact data to the ground. Observable and derived data from the SDS could provide information to models that are critical to understanding risks the small debris environment poses to spacecraft in low Earth orbit. The technology demonstrated by the SDS is a major step forward in monitoring and characterizing the space debris environment. This paper will address the technical performance of the SDS during its operational lifetime and its realization of technical and scientific goals. The SDS was intended to operate for 3 years; however, the payload incurred multiple anomalies during its operational life. Subsequently termed “Anomaly #1,” the first was the symptomatic loss of low data rate 1553 channel command and telemetry. The second, Anomaly #2, was loss of all low- and medium-data rate (Ethernet) telemetry. Anomaly #2 proved to be unrecoverable, leading to loss of the payload after approximately 26 days on-board the ISS. Therefore, this paper also addresses the anomalies that occurred during operation of the SDS, their attribution, and their resolution. Lessons learned are described when relevant to anomaly identification, attribution, and resolution.

Special technology and circuit architecture are of growing interest for implementation of circuits which operate at low supply voltages and consume low power levels without sacrificing performance[1]. Use of thin buried oxide SOI substrates is a primary approach to simultaneously achieve these goals. A significant aspect regarding SIMOX SOI for low voltage, low power applications is the reliability and performance of the thin buried oxide. In addition, when subjected to high total dose irradiation, the silicon islands within the BOX layer of SIMOX can store charges and significantly effect the back channel threshold voltages of devices. Thus, elimination of the islands within the buried oxide (BOX) layer is preferred in order to prevent leakage through these conductive islands and charge build-up within the buried oxide layer. A differential (2-step) ramp rate as applied to full and 100 nm BOX SIMOX was previously reported to play a significant role in the stoichiometry and island formation within the buried layer[2]. This paper focus is on the properties of a thin (120nm) buried oxide as a function of the anneal ramp rate and the temperature of anneal. In this research, we have found an improvement in the buried oxide stoichiometry with the use of a slower, singular ramp rate for specified thin buried oxides, with slower ramp rates and higher temperatures of anneal suggested for reducing the presence of Si islands within the BOX layer.