Noncommutative Dynamics of Random Operators

We continue our program of unifying general relativity and quantum mechanics in terms of a noncommutative algebra ${\cal A}$ on a transformation groupoid $\Gamma = E \times G$ where $E$ is the total space of a principal fibre bundle over spacetime, and $G$ a suitable group acting on $\Gamma$. We show that every $a \in {\cal A}$ defines a random operator, and we study the dynamics of such operators. In the noncommutative regime, there is no usual time but, on the strength of the Tomita-Takesaki theorem, there exists a one-parameter group of automorphisms of the algebra ${\cal A}$ which can be used to define a state dependent dynamics; i.e., the pair $({\cal A}, \phi)$, where $\phi$ is a state on ${\cal A}$, is a ``dynamic object''. Only if certain additional conditions are satisfied, the Connes-Nikodym-Radon theorem can be applied and the dependence on $\phi$ disappears. In these cases, the usual unitary quantum mechanical evolution is recovered. We also notice that the same pair $({\cal A}, \phi)$ defines the so-called free probability calculus, as developed by Voiculescu and others, with the state $\phi$ playing the role of the noncommutative probability measure. This shows that in the noncommutative regime dynamics and probability are unified. This also explains probabilistic properties of the usual quantum mechanics.Comment: 13 pages, LaTe

Scaling in the Positive Plaquette Model and Universality in SU(2) Lattice Gauge Theory

We investigate universality, scaling, the beta-function and the topological charge in the positive plaquette model for SU(2) lattice gauge theory. Comparing physical quantities, like the critical temperature, the string tension, glueball masses, and their ratios, we explore the effect of a complete suppression of a certain lattice artifact, namely the negative plaquettes, for SU(2) lattice gauge theory. Our result is that this modification does not change the continuum limit, i.e., the universality class. The positive plaquette model and the standard Wilson formulation describe the same physical situation. The approach to the continuum limit given by the beta-function in terms of the bare lattice coupling, however, is rather different: the beta-function of the positive plaquette model does not show a dip like the model with standard Wilson action.Comment: 35 pages, preprint numbers FSU-SCRI-94-71 and HU Berlin-IEP-94/1

Structural correlations in heterogeneous electron transfer at monolayer and multilayer graphene electrodes

As a new form of carbon, graphene is attracting intense interest as an electrode material with widespread applications. In the present study, the heterogeneous electron transfer (ET) activity of graphene is investigated using scanning electrochemical cell microscopy (SECCM), which allows electrochemical currents to be mapped at high spatial resolution across a surface for correlation with the corresponding structure and properties of the graphene surface. We establish that the rate of heterogeneous ET at graphene increases systematically with the number of graphene layers, and show that the stacking in multilayers also has a subtle influence on ET kinetics. © 2012 American Chemical Society

Mode of onset of torsade de pointes in congenital long QT syndrome

Objectives.We sought to describe the mode of onset of spontaneous torsade de pointes in the congenital long QT syndrome.Background.Contemporary classifications of the long QT syndrome (LQTS) refer to the congenital LQTS as “adrenergic dependent” and to the acquired LQTS as “pause dependent.” Overlap between these two categories has been recognized, and a subgroup of patients with “idiopathic pause-dependent torsade” has been described. However, it is not known how commonly torsade is preceded by pauses in the congenital LQTS.Methods.We reviewed the electrocardiograms (ECGs) of all our patients with congenital LQTS evaluated for syncope or sudden death (30 patients). Documentation of the onset of torsade de pointes was available for 15 patients. All these patients had “definitive LQTS” by accepted clinical and ECG criteria.Results.Pause-dependent torsade de pointes was clearly documented in 14 of the 15 patients (95% confidence interval 68% to 100%). The cycle length of the pause leading to torsade was 1.3 ± 0.2 times longer than the basic cycle length, and most pauses leading to torsade were unequivocally longer than the preceding basic cycle length (80% of pauses were >80 ms longer than the preceding cycle length).Conclusions.The “long-short” sequence, which has been recognized as a hallmark of torsade de pointes in the acquired LQTS, plays a major role in the genesis of torsade in the congenital LQTS as well. Our findings have important therapeutic implications regarding the use of pacemakers for prevention of torsade in the congenital LQTS

Universal geometric approach to uncertainty, entropy and information

It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a preferred and universal choice for characterising the inherent spread, dispersion, localisation, etc, of the ensemble. Remarkably, this unique "ensemble volume" is a simple function of the ensemble entropy, and hence provides a new geometric characterisation of the latter quantity. Applications include unified, volume-based derivations of the Holevo and Shannon bounds in quantum and classical information theory; a precise geometric interpretation of thermodynamic entropy for equilibrium ensembles; a geometric derivation of semi-classical uncertainty relations; a new means for defining classical and quantum localization for arbitrary evolution processes; a geometric interpretation of relative entropy; and a new proposed definition for the spot-size of an optical beam. Advantages of the ensemble volume over other measures of localization (root-mean-square deviation, Renyi entropies, and inverse participation ratio) are discussed.Comment: Latex, 38 pages + 2 figures; p(\alpha)->1/|T| in Eq. (72) [Eq. (A10) of published version

Electrochemistry at nanoscale electrodes : individual single-walled carbon nanotubes (SWNTs) and SWNT-templated metal nanowires

Individual nanowires (NWs) and native single-walled carbon nanotubes (SWNTs) can be readily used as well-defined nanoscale electrodes (NSEs) for voltammetric analysis. Here, the simple photolithography-free fabrication of submillimeter long Au, Pt, and Pd NWs, with sub-100 nm heights, by templated electrodeposition onto ultralong flow-aligned SWNTs is demonstrated. Both individual Au NWs and SWNTs are employed as NSEs for electron-transfer (ET) kinetic quantification, using cyclic voltammetry (CV), in conjunction with a microcapillary-based electrochemical method. A small capillary with internal diameter in the range 30–70 μm, filled with solution containing a redox-active mediator (FcTMA+ ((trimethylammonium)methylferrocene), Fe(CN)64–, or hydrazine) is positioned above the NSE, so that the solution meniscus completes an electrochemical cell. A 3D finite-element model, faithfully reproducing the experimental geometry, is used to both analyze the experimental CVs and derive the rate of heterogeneous ET, using Butler–Volmer kinetics. For a 70 nm height Au NW, intrinsic rate constants, k0, up to ca. 1 cm s–1 can be resolved. Using the same experimental configuration the electrochemistry of individual SWNTs can also be accessed. For FcTMA+/2+ electrolysis the simulated ET kinetic parameters yield very fast ET kinetics (k0 > 2 ± 1 cm s–1). Some deviation between the experimental voltammetry and the idealized model is noted, suggesting that double-layer effects may influence ET at the nanoscale

Free energy of an SU(2) monopole-antimonopole pair

We present a high-statistic numerical study of the free energy of a monopole-antimonopole pair in pure SU(2) theory. We find that the monopole-antimonopole interaction potential exhibits a screened behavior, as one would expect in presence of a monopole condensate. Screening occurs both in the low-temperature, confining phase of the theory, and in the high-temperature deconfined phase, with no evidence of a discontinuity of the screening mass across the transition. The mass of the object responsible for the screening at low temperature is approximately twice the established value for the lightest glueball, indicating a prevalent coupling to glueball excitations. At high temperature, the screening mass increases. We contrast the behavior of the quantum system with that of the corresponding classical system, where the monopole-antimonopole potential is of the Coulomb type.Comment: Latex, 22 pages, 8 figures. A mistake in the computer program implementing the multihistogram method has been corrected and all the affected numerical data have been revised. The main conclusions of the paper are unchanged, but the screening masses turn out somehow larger. (We thank Philippe de Forcrand for correspondence which helped us find the error.

Iodofiltic Acid I 123 (BMIPP) Fatty Acid Imaging Improves Initial Diagnosis in Emergency Department Patients With Suspected Acute Coronary Syndromes A Multicenter Trial

ObjectivesThe aim of this study was to assess the performance of β-methyl-p-[123I]-iodophenyl-pentadecanoic acid (BMIPP) single-photon emission computed tomography (SPECT) to detect acute coronary syndromes (ACS) in emergency department patients with chest pain.BackgroundEmergency department diagnosis of chest pain is problematic, often requiring prolonged observation and stress testing. BMIPP SPECT detects abnormalities in fatty acid metabolism resulting from myocardial ischemia, even many hours after symptom cessation.MethodsEmergency department patients with suspected ACS were enrolled at 50 centers. Patients received 5 mCi BMIPP within 30 h of symptom cessation. BMIPP SPECT images were interpreted semiquantitatively by 3 blinded readers. Initial clinical diagnosis was based on symptoms, initial electrocardiograms, and troponin, whereas the final diagnosis was based on all available data (including angiography and stress SPECT) but not BMIPP SPECT. Final diagnoses were adjudicated by a blinded committee as ACS, intermediate likelihood of ACS, or negative for ACS.ResultsA total of 507 patients were studied and efficacy was evaluated in 448 patients with sufficient data. The sensitivity of BMIPP by 3 blinded readers for a final diagnosis of ACS and intermediate likelihood of ACS was 71% (95% confidence interval [CI]: 64% to 79%), 74% (95% CI: 68% to 81%), and 69% (95% CI: 62% to 77%); the corresponding specificity of BMIPP was 67% (95% CI: 61% to 73%), 54% (95% CI: 48% to 60%), and 70% (95% CI: 64% to 76%). Compared with the initial diagnosis alone, BMIPP + initial diagnosis increased sensitivity from 43% to 81% (p < 0.001), negative predictive value from 62% to 83% (p < 0.001), and positive predictive value from 41% to 58% (p < 0.001), whereas specificity was unchanged (61% to 62%, p = NS).ConclusionsThe addition of BMIPP data to the initially available clinical information adds incremental value toward the early diagnosis of an ACS, potentially allowing determination of the presence or absence of ACS to be made earlier in the evaluation process. (Safety and Efficacy Iodofiltic Acid I 123 in the Treatment of Acute Coronary Syndrome [Zeus-ACS]; NCT00514501

A new view of electrochemistry at highly oriented pyrolytic graphite

Major new insights on electrochemical processes at graphite electrodes are reported, following extensive investigations of two of the most studied redox couples, Fe(CN)64–/3– and Ru(NH3)63+/2+. Experiments have been carried out on five different grades of highly oriented pyrolytic graphite (HOPG) that vary in step-edge height and surface coverage. Significantly, the same electrochemical characteristic is observed on all surfaces, independent of surface quality: initial cyclic voltammetry (CV) is close to reversible on freshly cleaved surfaces (>400 measurements for Fe(CN)64–/3– and >100 for Ru(NH3)63+/2+), in marked contrast to previous studies that have found very slow electron transfer (ET) kinetics, with an interpretation that ET only occurs at step edges. Significantly, high spatial resolution electrochemical imaging with scanning electrochemical cell microscopy, on the highest quality mechanically cleaved HOPG, demonstrates definitively that the pristine basal surface supports fast ET, and that ET is not confined to step edges. However, the history of the HOPG surface strongly influences the electrochemical behavior. Thus, Fe(CN)64–/3– shows markedly diminished ET kinetics with either extended exposure of the HOPG surface to the ambient environment or repeated CV measurements. In situ atomic force microscopy (AFM) reveals that the deterioration in apparent ET kinetics is coupled with the deposition of material on the HOPG electrode, while conducting-AFM highlights that, after cleaving, the local surface conductivity of HOPG deteriorates significantly with time. These observations and new insights are not only important for graphite, but have significant implications for electrochemistry at related carbon materials such as graphene and carbon nanotubes

The Finite Temperature SU(2) Savvidy Model with a Non-trivial Polyakov Loop

We calculate the complete one-loop effective potential for SU(2) gauge bosons at temperature T as a function of two variables: phi, the angle associated with a non-trivial Polyakov loop, and H, a constant background chromomagnetic field. Using techniques broadly applicable to finite temperature field theories, we develop both low and high temperature expansions. At low temperatures, the real part of the effective potential V_R indicates a rich phase structure, with a discontinuous alternation between confined (phi=pi) and deconfined phases (phi=0). The background field H moves slowly upward from its zero-temperature value as T increases, in such a way that sqrt(gH)/(pi T) is approximately an integer. Beyond a certain temperature on the order of sqrt(gH), the deconfined phase is always preferred. At high temperatures, where asymptotic freedom applies, the deconfined phase phi=0 is always preferred, and sqrt(gH) is of order g^2(T)T. The imaginary part of the effective potential is non-zero at the global minimum of V_R for all temperatures. A non-perturbative magnetic screening mass of the form M_m = cg^2(T)T with a sufficiently large coefficient c removes this instability at high temperature, leading to a stable high-temperature phase with phi=0 and H=0, characteristic of a weakly-interacting gas of gauge particles. The value of M_m obtained is comparable with lattice estimates.Comment: 28 pages, 5 eps figures; RevTeX 3 with graphic