On the constrained structure of duality symmetric Maxwell theory

The constrained structure of the duality invariant form of Maxwell theory is considered in the Hamiltonian formulation of Dirac as well as from the symplectic viewpoint. Compared to the former the latter approach is found to be more economical and elegant. Distinctions from the constrained analysis of the usual Maxwell theory are pointed out and their implications are also discussed.Comment: Latex, 12 page

Integrated Information Theory and Isomorphic Feed-Forward Philosophical Zombies

Any theory amenable to scientific inquiry must have testable consequences. This minimal criterion is uniquely challenging for the study of consciousness, as we do not know if it is possible to confirm via observation from the outside whether or not a physical system knows what it feels like to have an inside - a challenge referred to as the "hard problem" of consciousness. To arrive at a theory of consciousness, the hard problem has motivated the development of phenomenological approaches that adopt assumptions of what properties consciousness has based on first-hand experience and, from these, derive the physical processes that give rise to these properties. A leading theory adopting this approach is Integrated Information Theory (IIT), which assumes our subjective experience is a "unified whole", subsequently yielding a requirement for physical feedback as a necessary condition for consciousness. Here, we develop a mathematical framework to assess the validity of this assumption by testing it in the context of isomorphic physical systems with and without feedback. The isomorphism allows us to isolate changes in $\Phi$ without affecting the size or functionality of the original system. Indeed, we show that the only mathematical difference between a "conscious" system with $\Phi>0$ and an isomorphic "philosophical zombies" with $\Phi=0$ is a permutation of the binary labels used to internally represent functional states. This implies $\Phi$ is sensitive to functionally arbitrary aspects of a particular labeling scheme, with no clear justification in terms of phenomenological differences. In light of this, we argue any quantitative theory of consciousness, including IIT, should be invariant under isomorphisms if it is to avoid the existence of isomorphic philosophical zombies and the epistemological problems they pose.Comment: 13 page

Soft Tissue to Hard Tissue Advancement Ratios for Mandibular Elongation Using Distraction Osteogenesis in Children

Distraction osteogenesis is extensively used for the elongation of hypoplastic mandibles in children, yet the soft tissue profile response to this is not well understood. The pre- and posttreatment lateral cephalometric radiographs of 27 pediatric patients who underwent bilateral mandibular elongation using distraction osteogenesis were analyzed retrospectively to correlate horizontal soft tissue advancement with horizontal underlying bone advancement at B point and pogonion. Horizontal advancement (in millimeters) of bone and overlying soft tissue at these points was collected from the radiographs of each patient, and linear regression analysis was performed to determine the relationship of hard to soft tissue horizontal advancement at these points. A 1:0.90 mean ratio of bone to soft tissue advancement was observed at B point/labiomental sulcus and at pogonion/soft tissue pogonion (linear regression analysis demonstrated slopes [β1 values] of 0.94 and 0.92, respectively). These ratios were consistent throughout the sample population and are highly predictive of the soft tissue response that can be anticipated. Magnitude of advancement, age, and sex of the patient had no effect on these ratios in our population. This study assists with our understanding of the soft tissue response that accompanies bony elongation during distraction osteogenesis which will allow us to more effectively treatment plan the orthodontic and surgical intervention that will optimize the patients\u27 functional and esthetic outcome

Geometry of Discrete Quantum Computing

Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2^{n} infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields Fp^2 (based on primes p congruent to 3 mod{4}) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space CP{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p+1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to DCP{2^{n}-1}, the discrete analog of the complex projective space, which has p^{2^{n}-1} (p-1)\prod_{k=1}^{n-1} (p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field Fp^2 have p^{n} (p-1)^{n} unentangled states (the product of the tally for a single qubit) with purity 1, and they have p^{n+1}(p-1)(p+1)^{n-1} maximally entangled states with purity zero.Comment: 24 page

Spin filling of a quantum dot derived from excited-state spectroscopy

We study the spin filling of a semiconductor quantum dot using excited-state spectroscopy in a strong magnetic field. The field is oriented in the plane of the two-dimensional electron gas in which the dot is electrostatically defined. By combining the observation of Zeeman splitting with our knowledge of the absolute number of electrons, we are able to determine the ground state spin configuration for one to five electrons occupying the dot. For four electrons, we find a ground state spin configuration with total spin S=1, in agreement with Hund's first rule. The electron g-factor is observed to be independent of magnetic field and electron number.Comment: 11 pages, 7 figures, submitted to New Journal of Physics, focus issue on Solid State Quantum Informatio

Correction to the Moliere's formula for multiple scattering

The quasiclassical correction to the Moliere's formula for multiple scattering is derived. The consideration is based on the scattering amplitude, obtained with the first quasiclassical correction taken into account for arbitrary localized but not spherically symmetric potential. Unlike the leading term, the correction to the Moliere's formula contains the target density $n$ and thickness $L$ not only in the combination $nL$ (areal density). Therefore, this correction can be reffered to as the bulk density correction. It turns out that the bulk density correction is small even for high density. This result explains the wide region of applicability of the Moliere's formula.Comment: 6 pages, RevTe

Facile O-atom insertion into C-C and C-H bonds by a trinuclear copper complex designed to harness a singlet oxene

Two trinuclear copper [CuICuICuI(L)]1+ complexes have been prepared with the multidentate ligands (L) 3,3'-(1,4-diazepane-1,4-diyl)bis(1-((2-(dimethylamino)ethyl)(methyl)amino)propan-2-ol) (7-Me) and (3,3'-(1,4-diazepane-1,4-diyl)bis(1-((2-(diethylamino) ethyl)(ethyl) amino)propan-2-ol) (7-Et) as models for the active site of the particulate methane monooxygenase (pMMO). The ligands were designed to form the proper spatial and electronic geometry to harness a "singlet oxene," according to the mechanism previously suggested by our laboratory. Consistent with the design strategy, both [CuICuICuI(L)]1+ reacted with dioxygen to form a putative bis(µ3-oxo)CuIICuIICuIII species, capable of facile O-atom insertion across the central C-C bond of benzil and 2,3-butanedione at ambient temperature and pressure. These complexes also catalyze facile O-atom transfer to the C-H bond of CH3CN to form glycolonitrile. These results, together with our recent biochemical studies on pMMO, provide support for our hypothesis that the hydroxylation site of pMMO contains a trinuclear copper cluster that mediates C-H bond activation by a singlet oxene mechanism

Precision Studies of Duality in the 't Hooft Model

We address numerical aspects of local quark-hadron duality using the example of the exactly solvable 't Hooft model, two-dimensional QCD with N_c --> infinity. The primary focus of these studies is total semileptonic decay widths relevant for extracting |V_{cb}| and |V_{ub}|. We compare the exact channel-by-channel sum of exclusive modes to the corresponding rates obtained in the standard 1/m_Q expansion arising from the Operator Product Expansion. An impressive agreement sets in unexpectedly early, immediately after the threshold for the first hadronic excitation in the final state. Yet even at higher energy release it is possible to discern the seeds of duality-violating oscillations. We find the ``Small Velocity'' sum rules to be exceptionally well saturated already by the first excited state. We also obtain a convincing degree of duality in the differential distributions and in an analogue of R_{e^+e^-}(s). Finally, we discuss possible lessons for semileptonic decays of actual heavy quarks in QCD.Comment: 45 pages, 16 eps figures include