Optical metrics and birefringence of anisotropic media

The material tensor of linear response in electrodynamics is constructed out of products of two symmetric second rank tensor fields which in the approximation of geometrical optics and for uniaxial symmetry reduce to "optical" metrics, describing the phenomenon of birefringence. This representation is interpreted in the context of an underlying internal geometrical structure according to which the symmetric tensor fields are vectorial elements of an associated two-dimensional space.Comment: 24 pages, accepted for publication in GR

Kondo effect in multielectron quantum dots at high magnetic fields

We present a general description of low temperature transport through a quantum dot with any number of electrons at filling factor $1<\nu <2$. We provide a general description of a novel Kondo effect which is turned on by application of an appropriate magnetic field. The spin-flip scattering of carriers by the quantum dot only involves two states of the scatterer which may have a large spin. This process is described by spin-flip Hubbard operators, which change the angular momentum, leading to a Kondo Hamiltonian. We obtain antiferromagnetic exchange couplings depending on tunneling amplitudes and correlation effects. Since Kondo temperature has an exponential dependence on exchange couplings, quantitative variations of the parameters in different regimes have important experimental consequences. In particular, we discuss the {\it chess board} aspect of the experimental conductance when represented in a grey scale as a function of both the magnetic field and the gate potential affecting the quantum dot

The Two Dimensional Kondo Model with Rashba Spin-Orbit Coupling

We investigate the effect that Rashba spin-orbit coupling has on the low energy behaviour of a two dimensional magnetic impurity system. It is shown that the Kondo effect, the screening of the magnetic impurity at temperatures T < T_K, is robust against such spin-orbit coupling, despite the fact that the spin of the conduction electrons is no longer a conserved quantity. A proposal is made for how the spin-orbit coupling may change the value of the Kondo temperature T_K in such systems and the prospects of measuring this change are discussed. We conclude that many of the assumptions made in our analysis invalidate our results as applied to recent experiments in semi-conductor quantum dots but may apply to measurements made with magnetic atoms placed on metallic surfaces.Comment: 22 pages, 1 figure; reference update

Interference and interaction effects in multi-level quantum dots

Using renormalization group techniques, we study spectral and transport properties of a spinless interacting quantum dot consisting of two levels coupled to metallic reservoirs. For strong Coulomb repulsion $U$ and an applied Aharonov-Bohm phase $\phi$, we find a large direct tunnel splitting $|\Delta|\sim (\Gamma/\pi)|\cos(\phi/2)|\ln(U/\omega_c)$ between the levels of the order of the level broadening $\Gamma$. As a consequence we discover a many-body resonance in the spectral density that can be measured via the absorption power. Furthermore, for $\phi=\pi$, we show that the system can be tuned into an effective Anderson model with spin-dependent tunneling.Comment: 5 pages, 4 figures included, typos correcte

Derivation and validation of a prognostic model for postoperative risk stratification of critically ill patients with faecal peritonitis

Background Prognostic scores and models of illness severity are useful both clinically and for research. The aim of this study was to develop two prognostic models for the prediction of long-term (6 months) and 28-day mortality of postoperative critically ill patients with faecal peritonitis (FP). Methods Patients admitted to intensive care units with faecal peritonitis and recruited to the European GenOSept study were divided into a derivation and a geographical validation subset; patients subsequently recruited to the UK GAinS study were used for temporal validation. Using all 50 clinical and laboratory variables available on day 1 of critical care admission, Cox proportional hazards regression was fitted to select variables for inclusion in two prognostic models, using stepwise selection and nonparametric bootstrapping sampling techniques. Using Area under the receiver operating characteristic curve (AuROC) analysis, the performance of the models was compared to SOFA and APACHE II. Results Five variables (age, SOFA score, lowest temperature, highest heart rate, haematocrit) were entered into the prognostic models. The discriminatory performance of the 6-month prognostic model yielded an AuROC 0.81 (95% CI 0.76–0.86), 0.73 (95% CI 0.69–0.78) and 0.76 (95% CI 0.69–0.83) for the derivation, geographic and temporal external validation cohorts, respectively. The 28-day prognostic tool yielded an AuROC 0.82 (95% CI 0.77–0.88), 0.75 (95% CI 0.69–0.80) and 0.79 (95% CI 0.71–0.87) for the same cohorts. These AuROCs appeared consistently superior to those obtained with the SOFA and APACHE II scores alone. Conclusions The two prognostic models developed for 6-month and 28-day mortality prediction in critically ill septic patients with FP, in the postoperative phase, enhanced the day one SOFA score’s predictive utility by adding a few key variables: age, lowest recorded temperature, highest recorded heart rate and haematocrit. External validation of their predictive capability in larger cohorts is needed, before introduction of the proposed scores into clinical practice to inform decision making and the design of clinical trials

The effect of two-temperature post-shock accretion flow on the linear polarization pulse in magnetic cataclysmic variables

The temperatures of electrons and ions in the post-shock accretion region of a magnetic cataclysmic variable (mCV) will be equal at sufficiently high mass flow rates or for sufficiently weak magnetic fields. At lower mass flow rates or in stronger magnetic fields, efficient cyclotron cooling will cool the electrons faster than the electrons can cool the ions and a two-temperature flow will result. Here we investigate the differences in polarized radiation expected from mCV post-shock accretion columns modeled with one- and two-temperature hydrodynamics. In an mCV model with one accretion region, a magnetic field >~30 MG and a specific mass flow rate of ~0.5 g/cm/cm/s, along with a relatively generic geometric orientation of the system, we find that in the ultraviolet either a single linear polarization pulse per binary orbit or two pulses per binary orbit can be expected, depending on the accretion column hydrodynamic structure (one- or two-temperature) modeled. Under conditions where the physical flow is two-temperature, one pulse per orbit is predicted from a single accretion region where a one-temperature model predicts two pulses. The intensity light curves show similar pulse behavior but there is very little difference between the circular polarization predictions of one- and two-temperature models. Such discrepancies indicate that it is important to model some aspect of two-temperature flow in indirect imaging procedures, like Stokes imaging, especially at the edges of extended accretion regions, were the specific mass flow is low, and especially for ultraviolet data.Comment: Accepted for publication in Astrophysics & Space Scienc

The embedding method beyond the single-channel case: Two-mode and Hubbard chains

We investigate the relationship between persistent currents in multi-channel rings containing an embedded scatterer and the conductance through the same scatterer attached to leads. The case of two uncoupled channels corresponds to a Hubbard chain, for which the one-dimensional embedding method is readily generalized. Various tests are carried out to validate this new procedure, and the conductance of short one-dimensional Hubbard chains attached to perfect leads is computed for different system sizes and interaction strengths. In the case of two coupled channels the conductance can be obtained from a statistical analysis of the persistent current or by reducing the multi-channel scattering problem to several single-channel setups.Comment: 14 pages, 13 figures, submitted for publicatio

Electron spin as a spectrometer of nuclear spin noise and other fluctuations

This chapter describes the relationship between low frequency noise and coherence decay of localized spins in semiconductors. Section 2 establishes a direct relationship between an arbitrary noise spectral function and spin coherence as measured by a number of pulse spin resonance sequences. Section 3 describes the electron-nuclear spin Hamiltonian, including isotropic and anisotropic hyperfine interactions, inter-nuclear dipolar interactions, and the effective Hamiltonian for nuclear-nuclear coupling mediated by the electron spin hyperfine interaction. Section 4 describes a microscopic calculation of the nuclear spin noise spectrum arising due to nuclear spin dipolar flip-flops with quasiparticle broadening included. Section 5 compares our explicit numerical results to electron spin echo decay experiments for phosphorus doped silicon in natural and nuclear spin enriched samples.Comment: Book chapter in "Electron spin resonance and related phenomena in low dimensional structures", edited by Marco Fanciulli. To be published by Springer-Verlag in the TAP series. 35 pages, 9 figure

Verified lifting of stencil computations

This paper demonstrates a novel combination of program synthesis and verification to lift stencil computations from low-level Fortran code to a high-level summary expressed using a predicate language. The technique is sound and mostly automated, and leverages counter-example guided inductive synthesis (CEGIS) to find provably correct translations. Lifting existing code to a high-performance description language has a number of benefits, including maintainability and performance portability. For example, our experiments show that the lifted summaries can enable domain specific compilers to do a better job of parallelization as compared to an off-the-shelf compiler working on the original code, and can even support fully automatic migration to hardware accelerators such as GPUs. We have implemented verified lifting in a system called STNG and have evaluated it using microbenchmarks, mini-apps, and real-world applications. We demonstrate the benefits of verified lifting by first automatically summarizing Fortran source code into a high-level predicate language, and subsequently translating the lifted summaries into Halide, with the translated code achieving median performance speedups of 4.1X and up to 24X for non-trivial stencils as compared to the original implementation.United States. Department of Energy. Office of Science (Award DE-SC0008923)United States. Department of Energy. Office of Science (Award DE-SC0005288

Atmospheric Methane : Comparison Between Methane's Record in 2006–2022 and During Glacial Terminations

Atmospheric methane's rapid growth from late 2006 is unprecedented in the observational record. Assessment of atmospheric methane data attributes a large fraction of this atmospheric growth to increased natural emissions over the tropics, which appear to be responding to changes in anthropogenic climate forcing. Isotopically lighter measurements of (Figure presented.) are consistent with the recent atmospheric methane growth being mainly driven by an increase in emissions from microbial sources, particularly wetlands. The global methane budget is currently in disequilibrium and new inputs are as yet poorly quantified. Although microbial emissions from agriculture and waste sources have increased between 2006 and 2022 by perhaps 35 Tg/yr, with wide uncertainty, approximately another 35–45 Tg/yr of the recent net growth in methane emissions may have been driven by natural biogenic processes, especially wetland feedbacks to climate change. A model comparison shows that recent changes may be comparable or greater in scale and speed than methane's growth and isotopic shift during past glacial/interglacial termination events. It remains possible that methane's current growth is within the range of Holocene variability, but it is also possible that methane's recent growth and isotopic shift may indicate a large-scale reorganization of the natural climate and biosphere is under way