The Equivalence Postulate of Quantum Mechanics

The Equivalence Principle (EP), stating that all physical systems are connected by a coordinate transformation to the free one with vanishing energy, univocally leads to the Quantum Stationary HJ Equation (QSHJE). Trajectories depend on the Planck length through hidden variables which arise as initial conditions. The formulation has manifest p-q duality, a consequence of the involutive nature of the Legendre transform and of its recently observed relation with second-order linear differential equations. This reflects in an intrinsic psi^D-psi duality between linearly independent solutions of the Schroedinger equation. Unlike Bohm's theory, there is a non-trivial action even for bound states. No use of any axiomatic interpretation of the wave-function is made. Tunnelling is a direct consequence of the quantum potential which differs from the usual one and plays the role of particle's self-energy. The QSHJE is defined only if the ratio psi^D/psi is a local self-homeomorphism of the extended real line. This is an important feature as the L^2 condition, which in the usual formulation is a consequence of the axiomatic interpretation of the wave-function, directly follows as a basic theorem which only uses the geometrical gluing conditions of psi^D/psi at q=\pm\infty as implied by the EP. As a result, the EP itself implies a dynamical equation that does not require any further assumption and reproduces both tunnelling and energy quantization. Several features of the formulation show how the Copenhagen interpretation hides the underlying nature of QM. Finally, the non-stationary higher dimensional quantum HJ equation and the relativistic extension are derived.Comment: 1+3+140 pages, LaTeX. Invariance of the wave-function under the action of SL(2,R) subgroups acting on the reduced action explicitly reveals that the wave-function describes only equivalence classes of Planck length deterministic physics. New derivation of the Schwarzian derivative from the cocycle condition. "Legendre brackets" introduced to further make "Legendre duality" manifest. Introduction now contains examples and provides a short pedagogical review. Clarifications, conclusions, ackn. and references adde

Photothermal Desorption of Single-Walled Carbon Nanotubes and Coconut Shell-Activated Carbons Using a Continuous Light Source for Application in Air Sampling

Many techniques exist to measure airborne volatile organic compounds (VOCs), each with differing advantages; sorbent sampling is compact, versatile, has good sample stability, and is the preferred technique for collecting VOCs for hygienists. Development of a desorption technique that allows multiple analyses per sample (similar to chemical desorption) with enhanced sensitivity (similar to thermal desorption) would be helpful to field hygienists. In this study, activated carbon (AC) and single-walled carbon nanotubes (SWNT) were preloaded with toluene vapor and partially desorbed with light using a common 12-V DC, 50-W incandescent/halogen lamp. A series of experimental chamber configurations were explored starting with a 500-ml chamber under static conditions, then with low ventilation and high ventilation, finally a 75-ml high ventilation chamber was evaluated. When preloaded with toluene and irradiated at the highest lamp setting for 4min, AC desorbed 13.9, 18.5, 23.8, and 45.9% of the loaded VOC mass, in each chamber configuration, respectively; SWNT desorbed 25.2, 24.3, 37.4, and 70.5% of the loaded VOC mass, respectively. SWNT desorption was significantly greater than AC in all test conditions (P = 0.02?<0.0001) demonstrating a substantial difference in sorbent performance. When loaded with 0.435mg toluene and desorbed at the highest lamp setting for 4min in the final chamber design, the mean desorption for AC was 45.8% (39.7, 52.0) and SWNT was 72.6% (68.8, 76.4) (mean represented in terms of 95% confidence interval). All desorption measurements were obtained using a field grade photoionization detector; this demonstrates the potential of using this technique to perform infield prescreening of VOC samples for immediate exposure feedback and in the analytical lab to introduce sample to a gas chromatograph for detailed analysis of the sampleFil: Floyd, Evan L.. Oklahoma State University; Estados UnidosFil: Sapag, Manuel Karim. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Física Aplicada; ArgentinaFil: Oh, Jonghwa. University Of Alabama At Birmingahm; Estados UnidosFil: Lungu, Claudiu T.. University Of Alabama At Birmingahm; Estados Unido

Dvoretzky type theorems for multivariate polynomials and sections of convex bodies

In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on $\mathbb R^n$, and improve bounds on the number $n(d,k)$ in the analogous conjecture for odd degrees $d$ (this case is known as the Birch theorem) and complex polynomials. We also consider a stronger conjecture on the homogeneous polynomial fields in the canonical bundle over real and complex Grassmannians. This conjecture is much stronger and false in general, but it is proved in the cases of $d=2$ (for $k$'s of certain type), odd $d$, and the complex Grassmannian (for odd and even $d$ and any $k$). Corollaries for the John ellipsoid of projections or sections of a convex body are deduced from the case $d=2$ of the polynomial field conjecture

Turning points: the personal and professional circumstances that lead academics to become middle managers

In the current higher education climate, there is a growing perception that the pressures associated with being an academic middle manager outweigh the perceived rewards of the position. This article investigates the personal and professional circumstances that lead academics to become middle managers by drawing on data from life history interviews undertaken with 17 male and female department heads from a range of disciplines, in a post-1992 UK university. The data suggests that experiencing conflict between personal and professional identities, manifested through different socialization experiences over time, can lead to a ‘turning point’ and a decision that affects a person’s career trajectory. Although the results of this study cannot be generalized, the findings may help other individuals and institutions move towards a firmer understanding of the academic who becomes head of department—in relation to theory, practice and research

The Quantum Reduced Action In Higher Dimensions

The solution with respect to the reduced action of the one-dimensional stationary quantum Hamilton-Jacobi equation is well known in the literature. The extension to higher dimensions in the separated variable case was proposed in contradictory formulations. In this paper we provide new insights into the construction of the reduced action. In particular, contrary to the classical mechanics case, we analytically show that the reduced action constructed as a sum of one variable functions does not contain a complete information about the quantum motion. In the same context, we also make some observations about recent results concerning quantum trajectories. Finally, we will examine the conditions in which microstates appear even in the case where the wave function is complex.Comment: 12 pages, no figur

In Situ Instrumentation for Sub-Surface Planetary Geochemistry

Novel instrumentation is under development at NASA's Goddard Space Flight Center, building upon earth-based techniques for hostile environments, to infer geochemical processes important to formation and evolution of solid bodies in our Solar System. A prototype instrument, the Pulsed Neutron Generator Gamma Ray and Neutron Detectors (PNG-GRAND), has a 14 MeV pulsed neutron generator coupled with gamma ray and neutron detectors to measure quantitative elemental concentrations and bulk densities of a number of major, minor and trace elements at or below the surfaces with approximately a meter-sized spatial resolution down to depths of about 50 cm without the need to drill. PNG-GRAND's in situ a meter-scale measurements and adaptability to a variety of extreme space environments will complement orbital kilometer-scale and in-situ millimeter scale elemental and mineralogical measurements to provide a more complete picture of the geochemistry of planets, moons, asteroids and comets

Active Neutron and Gamma Ray Instrumentation for In Situ Planetary Science Applications

The Pulsed Neutron Generator-Gamma Ray And Neutron Detectors (PNG-GRAND) experiment is an innovative application of the active neutron-gamma ray technology so successfully used in oil field well logging and mineral exploration on Earth. The objective of our active neutron-gamma ray technology program at NASA Goddard Space Flight Center (NASA-GSFC) is to bring the PNG-GRAND instrument to the point where it can be flown on a variety of surface lander or rover missions to the Moon, Mars, Menus, asteroids, comets and the satellites of the outer planets. Gamma-Ray Spectrometers (GRS) have been incorporated into numerous orbital planetary science missions and, especially its the case of the Mars Odyssey GRS, have contributed detailed maps of the elemental composition over the entire surface of Mars. However, orbital gamma ray measurements have low spatial sensitivity (100's of km) due to their low surface emission rates from cosmic rays and subsequent need to be averaged over large surface areas. PNG-GRAND overcomes this impediment by incorporating a powerful neutron excitation source that permits high sensitivity surface and subsurface measurements of bulk elemental compositions. PNG-GRAND combines a pulsed neutron generator (PNG) with gamma ray and neutron detectors to produce a landed instrument to determine subsurface elemental composition without needing to drill into a planet's surface a great advantage in mission design. We are currently testing PNG-GRAND prototypes at a unique outdoor neutron instrumentation test facility recently constructed at NASA/GSFC that consists of a 2 m x 2 in x 1 m granite structure placed outdoors in an empty field. Because an independent trace elemental analysis has been performed on the material, this granite sample is a known standard with which to compare both Monte Carlo simulations and our experimentally measured elemental composition data. We will present data from operating PNG-GRAND in various experimental configurations on a known sample in a geometry that is identical to that on a planetary surface. We will also illustrate the use of gamma ray timing techniques to improve sensitivity and will compare the material composition results from our experiments to both an independent laboratory elemental composition analysis and MCNPX computer modeling results

Planetary Geochemistry Using Active Neutron and Gamma Ray Instrumentation

The Pulsed Neutron Generator-Gamma Ray And Neutron Detector (PNG-GRAND) experiment is an innovative application of the active neutron-gamma ray technology so successfully used in oil field well logging and mineral exploration on Earth, The objective of our active neutron-gamma ray technology program at NASA Goddard Space Flight Center (NASA/GSFC) is to bring the PNG-GRAND instrument to the point where it can be flown on a variety of surface lander or rover missions to the Moon, Mars, Venus, asterOIds, comets and the satellites of the outer planets, Gamma-Ray Spectrometers have been incorporated into numerous orbital planetary science missions and, especially in the case of Mars Odyssey, have contributed detailed maps of the elemental composition over the entire surface of Mars, Neutron detectors have also been placed onboard orbital missions such as the Lunar Reconnaissance Orbiter and Lunar Prospector to measure the hydrogen content of the surface of the moon, The DAN in situ experiment on the Mars Science Laboratory not only includes neutron detectors, but also has its own neutron generator, However, no one has ever combined the three into one instrument PNG-GRAND combines a pulsed neutron generator (PNG) with gamma ray and neutron detectors to produce a landed instrument that can determine subsurface elemental composition without drilling. We are testing PNG-GRAND at a unique outdoor neutron instrumentation test facility recently constructed at NASA/GSFC that consists of a 2 m x 2 m x 1 m granite structure in an empty field, We will present data from the operation of PNG-GRAND in various experimental configurations on a known sample in a geometry that is identical to that which can be achieved on a planetary surface. We will also compare the material composition results inferred from our experiments to both an independent laboratory elemental composition analysis and MCNPX computer modeling results

A Unique Outside Neutron and Gamma Ray Instrumentation Development Test Facility at NASA's Goddard Space Flight Center

An outside neutron and gamma ray instrumentation test facility has been constructed at NASA's Goddard Space Flight Center (GSFC) to evaluate conceptual designs of gamma ray and neutron systems that we intend to propose for future planetary lander and rover missions. We will describe this test facility and its current capabilities for operation of planetary in situ instrumentation, utilizing a l4 MeV pulsed neutron generator as the gamma ray excitation source with gamma ray and neutron detectors, in an open field with the ability to remotely monitor and operate experiments from a safe distance at an on-site building. The advantage of a permanent test facility with the ability to operate a neutron generator outside and the flexibility to modify testing configurations is essential for efficient testing of this type of technology. Until now, there have been no outdoor test facilities for realistically testing neutron and gamma ray instruments planned for solar system exploratio

Drastic Circuit Depth Reductions with Preserved Adversarial Robustness by Approximate Encoding for Quantum Machine Learning

Quantum machine learning (QML) is emerging as an application of quantum computing with the potential to deliver quantum advantage, but its realisation for practical applications remains impeded by challenges. Amongst those, a key barrier is the computationally expensive task of encoding classical data into a quantum state, which could erase any prospective speed-ups over classical algorithms. In this work, we implement methods for the efficient preparation of quantum states representing encoded image data using variational, genetic and matrix product state based algorithms. Our results show that these methods can approximately prepare states to a level suitable for QML using circuits two orders of magnitude shallower than a standard state preparation implementation, obtaining drastic savings in circuit depth and gate count without unduly sacrificing classification accuracy. Additionally, the QML models trained and evaluated on approximately encoded data display an increased robustness to adversarially generated input data perturbations. This partial alleviation of adversarial vulnerability, possible due to the "drowning out" of adversarial perturbations while retaining the meaningful large-scale features of the data, constitutes a considerable benefit for approximate state preparation in addition to lessening the requirements of the quantum hardware. Our results, based on simulations and experiments on IBM quantum devices, highlight a promising pathway for the future implementation of accurate and robust QML models on complex datasets relevant for practical applications, bringing the possibility of NISQ-era QML advantage closer to reality.Comment: 14 pages, 8 figure