Dirac Quantization of Parametrized Field Theory

Parametrized field theory (PFT) is free field theory on flat spacetime in a diffeomorphism invariant disguise. It describes field evolution on arbitrary foliations of the flat spacetime instead of only the usual flat ones, by treating the `embedding variables' which describe the foliation as dynamical variables to be varied in the action in addition to the scalar field. A formal Dirac quantization turns the constraints of PFT into functional Schrodinger equations which describe evolution of quantum states from an arbitrary Cauchy slice to an infinitesimally nearby one.This formal Schrodinger picture- based quantization is unitarily equivalent to the standard Heisenberg picture based Fock quantization of the free scalar field if scalar field evolution along arbitrary foliations is unitarily implemented on the Fock space. Torre and Varadarajan (TV) showed that for generic foliations emanating from a flat initial slice in spacetimes of dimension greater than 2, evolution is not unitarily implemented, thus implying an obstruction to Dirac quantization. We construct a Dirac quantization of PFT,unitarily equivalent to the standard Fock quantization, using techniques from Loop Quantum Gravity (LQG) which are powerful enough to super-cede the no- go implications of the TV results. The key features of our quantization include an LQG type representation for the embedding variables, embedding dependent Fock spaces for the scalar field, an anomaly free representation of (a generalization of) the finite transformations generated by the constraints and group averaging techniques. The difference between 2 and higher dimensions is that in the latter, only finite gauge transformations are defined in the quantum theory, not the infinitesimal ones.Comment: 33 page

Flexible VWAP Executions in Electronic Trading

For the execution of large equity orders, institutional investors often use the Volume Weighted Average Price (VWAP) as a benchmark to measure execution quality. To achieve this, they have the possibility to either cross their orders in a nonintermediated electronic system or to submit a VWAP agency order to a broker that executes the orders manually. Though more expensive in explicit costs, agency VWAP is still more attractive to investors than VWAP crossings, in particular due to higher flexibility. This work proposes a new electronic crossing model addressing and solving the flexibility restrictions present in today’s VWAP crossing

Critical Crossover Between Yosida-Kondo Dominant Regime and Magnetic Frustration Dominant Regime in the System of a Magnetic Trimer on a Metal Surface

Quantum Monte Carlo simulations were carried out for the system of a magnetic trimer on a metal surface. The magnetic trimer is arranged in two geometric configurations, viz., isosceles and equilateral triangles. The calculated spectral density and magnetic susceptibility show the existence of two phases: Yosida-Kondo dominant phase and magnetic frustration dominant phase. Furthermore, a critical transition between these two phases can be induced by changing the configuration of the magnetic trimers from isosceles to equilateral triangle.Comment: 8 pages, 4 figures; accepted for publication in J. Phys. Soc. Jp

Scattering Theory of Kondo Mirages and Observation of Single Kondo Atom Phase Shift

We explain the origin of the Kondo mirage seen in recent quantum corral Scanning Tunneling Microscope (STM) experiments with a scattering theory of electrons on the surfaces of metals. Our theory combined with experimental data provides the first direct observation of a single Kondo atom phase shift. The Kondo mirage at the empty focus of an elliptical quantum corral is shown to arise from multiple electron bounces off the walls of the corral in a manner analagous to the formation of a real image in optics. We demonstrate our theory with direct quantitive comparision to experimental data.Comment: 13 pages; significant clarifications of metho

Functional evolution of quantum cylindrical waves

Kucha{\v{r}} showed that the quantum dynamics of (1 polarization) cylindrical wave solutions to vacuum general relativity is determined by that of a free axially-symmetric scalar field along arbitrary axially-symmetric foliations of a fixed flat 2+1 dimensional spacetime. We investigate if such a dynamics can be defined {\em unitarily} within the standard Fock space quantization of the scalar field. Evolution between two arbitrary slices of an arbitrary foliation of the flat spacetime can be built out of a restricted class of evolutions (and their inverses). The restricted evolution is from an initial flat slice to an arbitrary (in general, curved) slice of the flat spacetime and can be decomposed into (i) `time' evolution in which the spatial Minkowskian coordinates serve as spatial coordinates on the initial and the final slice, followed by (ii) the action of a spatial diffeomorphism of the final slice on the data obtained from (i). We show that although the functional evolution of (i) is unitarily implemented in the quantum theory, generic spatial diffeomorphisms of (ii) are not. Our results imply that a Tomanaga-Schwinger type functional evolution of quantum cylindrical waves is not a viable concept even though, remarkably, the more limited notion of functional evolution in Kucha{\v{r}}'s `half parametrized formalism' is well-defined.Comment: Replaced with published versio

Relation of delayed recovery of myocardial function after takotsubo cardiomyopathy to subsequent quality of life

Takotsubo cardiomyopathy (TTC) has generally been regarded as a relatively transient disorder, characterized by reversible regional left ventricular systolic dysfunction. However, most patients with TTC experience prolonged lassitude or dyspnea after acute attacks. Although this might reflect continued emotional stress, myocardial inflammation and accentuated brain-type natriuretic peptide (BNP) release persist for at least 3 months. We therefore tested the hypotheses that this continued inflammation is associated with (1) persistent contractile dysfunction and (2) consequent impairment of quality of life. Echocardiographic parameters (global longitudinal strain [GLS], longitudinal strain rate [LSR], and peak apical twist [AT]) were compared acutely and after 3 months in 36 female patients with TTC and 19 age-matched female controls. Furthermore, correlations were sought between putative functional anomalies, inflammatory markers (T2 score on cardiovascular magnetic resonance, plasma NT-proBNP, and high-sensitivity C-reactive protein levels), and the physical composite component of SF36 score (SF36-PCS). In TTC cases, left ventricular ejection fraction returned to normal within 3 months. GLS, LSR, and AT improved significantly over 3-month recovery, but GLS remained reduced compared to controls even at follow-up (-17.9 ± 3.1% vs -20.0 ± 1.8%, p = 0.003). Impaired GLS at 3 months was associated with both persistent NT-proBNP elevation (p = 0.03) and reduced SF36-PCS at ≥3 months (p = 0.04). In conclusion, despite normalization of left ventricular ejection fraction, GLS remains impaired for at least 3 months, possibly as a result of residual myocardial inflammation. Furthermore, perception of impaired physical exercise capacity ≥3 months after TTC may be explained by persistent myocardial dysfunction

MODIS Instrument Operation and Calibration Improvements

Terra and Aqua MODIS have successfully operated for over 14 and 12 years since their respective launches in 1999 and 2002. The MODIS on-orbit calibration is performed using a set of on-board calibrators, which include a solar diffuser for calibrating the reflective solar bands (RSB) and a blackbody for the thermal emissive bands (TEB). On-orbit changes in the sensor responses as well as key performance parameters are monitored using the measurements of these on-board calibrators. This paper provides an overview of MODIS on-orbit operation and calibration activities, and instrument long-term performance. It presents a brief summary of the calibration enhancements made in the latest MODIS data collection 6 (C6). Future improvements in the MODIS calibration and their potential applications to the S-NPP VIIRS are also discussed

Polymer quantization of the free scalar field and its classical limit

Building on prior work, a generally covariant reformulation of free scalar field theory on the flat Lorentzian cylinder is quantized using Loop Quantum Gravity (LQG) type `polymer' representations. This quantization of the {\em continuum} classical theory yields a quantum theory which lives on a discrete spacetime lattice. We explicitly construct a state in the polymer Hilbert space which reproduces the standard Fock vacuum- two point functions for long wavelength modes of the scalar field. Our construction indicates that the continuum classical theory emerges under coarse graining. All our considerations are free of the "triangulation" ambiguities which plague attempts to define quantum dynamics in LQG. Our work constitutes the first complete LQG type quantization of a generally covariant field theory together with a semi-classical analysis of the true degrees of freedom and thus provides a perfect infinite dimensional toy model to study open issues in LQG, particularly those pertaining to the definition of quantum dynamics.Comment: 58 page

Microscopic theory for quantum mirages in quantum corrals

Scanning tunneling microscopy permits to image the Kondo resonance of a single magnetic atom adsorbed on a metallic surface. When the magnetic impurity is placed at the focus of an elliptical quantum corral, a Kondo resonance has been recently observed both on top of the impurity and on top of the focus where no magnetic impurity is present. This projection of the Kondo resonance to a remote point on the surface is referred to as quantum mirage. We present a quantum mechanical theory for the quantum mirage inside an ideal quantum corral and predict that the mirage will occur in corrals with shapes other than elliptical