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In this paper, we construct anticliques for noncommutative operator graphs generated by generalized Pauli matrices. It is shown that application of entangled states for the construction of the code space K allows one to substantially increase the dimension of a noncommutative operator graph for which the projection on K is an anticlique.
Quaternions discovered by W. R. Hamilton made a great contribution to the progress in noncommutative algebra and vector analysis. However, the analysis of quaternion functions has not been duly developed. The matter is that the notion of a derivative of quaternion functions of a quaternion variable has not been known until recently. The author has succeeded in improving the situation. The present work contains an account of the results obtained by him in this direction. The notion of an ℍ-derivative is introduced for quaternion functions of a quaternion variable. The existence of an ℍ-derivative of elementary functions is established retaining the well-known formulas for the corresponding functions from complex (real) analysis. The rules on the ℍ-differentiation of a sum, a product, and an inverse function are formulated and proved. Necessary and sufficient conditions for the existence of an ℍ-derivative are established. The notions of ℂ{sup 2}-differentiation and ℂ{sup 2}-holomorphy are introduced for quaternion functions of a quaternion variable. Three equivalent conditions are found, each of them being a necessary and sufficient one for ℂ{sup 2}-differentiation. Representations by an integral and a power series are given for ℂ{sup 2}-holomorphic functions. It is proved that the harmonicity of functions f(z), z · f(z), and f(z) · z is the necessary and sufficient condition for a function f to be Fueter-regular.
Kraus representation of quantum information transfer channels is widely used in practice. We present examples of Kraus decompositions for channels that possess the covariance property with respect to the maximal commutative group of unitary operators. We show that in some problems (for example, the problem on the estimate of the minimal output entropy of the channel), the choice of a Kraus representation with nonminimal number of Kraus operators is relevant. We also present certain algebraic properties of noncommutative operator graphs generated by Kraus operators for the case of quantum channels that demonstrate the superactivation phenomenon.
The Bloch equation in the Heisenberg–Weyl group is considered. A λ-representation of the Lie algebra of a Heisenberg–Weyl group of arbitrary dimensionality is constructed, and an expression for the statistical sum in the Heisenberg–Weyl group is obtained. Expressions for the statistical sum of the Heisenberg–Weyl group and other thermodynamic quantities are analyzed.
The azimuthal correlation belongs to a class of polarization observables which vanishes at the Born term level in the standard model for the semileptonic rest frame decay of a polarized top quark t(↑)→bW{sup +}→bℓ{sup +}υ{sub ℓ}. In this frame, the azimuthal correlation is defined between the planes formed by the vectors ( p-vector {sub ℓ}, p-vector {sub X{sub b}}) and ( p-vector {sub ℓ}, P-vector {sub t}). We calculate the azimuthal correlation function of polarized top quark in the framework of the noncommutative standard model for the first time. We find that this observable is nonzero in the leading order of noncommutative space–time. Further the appearance of the oscillatory azimuthal distribution of decay rate provides a practical possibility to test the noncommutativity in particle colliders.
In this paper, noncommutative gravity is treated as a gauge theory of the noncommutative SO(2,3){sub ⋆} group, while the noncommutativity is canonical. The Seiberg–Witten (SW) map is used to express noncommutative fields in terms of the corresponding commutative fields. In addition to pure gravity, we consider couplings to matter fields, in particular, to the Dirac and U(1) gauge field. The analysis can be extended to non Abelian gauge fields and scalar fields.
The level of access to opportunities for a location can be quantified in the amount of time it takes to travel from a departure point to the destinations that somebody would want or need to visit. Isochrone maps are geometric representations of the area accessible from a departure point within a set amount of time. Informed in part by the National Household Travel Survey, this report merges location data for amenities and opportunities across six frequent destination categories – employment, education, health, food, community, and transportation – with isochrone maps generated by the TravelTime API, whose departure points are census tract population-weighted centroids. Using a “Points-In-Polygon” analysis, destinations that fall within a census tract’s isochrone are tallied as accessible from the region within one of three time thresholds: 15-, 30-, and 45-minutes by the walking, cycling, public transit, and driving modes of travel. We find that access to a high number of jobs within a typical commute duration is negatively correlated with annual household vehicle miles traveled (VMT). The spatial distribution of our data suggests that the high household VMT frequently seen surrounding the edges of major cities may be related to worker commutes into the city core, and that the high household VMT frequently seen in rural tracts may be related to the longer travel distances required to access a variety of key opportunities from these areas.
Community planning needs, criteria, and other considerations such as intermodal coordination and regulatory requirements, for rotorcraft and fixed wing commuter air transportation were identified. A broad range of community planning guidelines, issues, and information which can be used to: (1) direct anticipated aircraft technological improvements; (2) assist planners in identifying and evaluating the opportunities and tradeoffs presented by rotorcraft and commuter aircraft options relative to other modes; and (3) increase communication between aircraft technologists and planners for the purpose of on going support in capitalizing on rotorcraft and commuter air opportunities are provided. The primary tool for identifying and analyzing planning requirements was a detailed questionnaire administered to a selected sample of 55 community planners and other involved in planning for helicopters and commuter aviation.
This paper examines commuting options for an underserved neighborhood in Columbus, Ohio to a major employment center. The analysis is based on an emerging metric called the Mobility Energy Productivity (MEP) metric developed by the National Renewable Energy Laboratory (NREL) on behalf the Department of Energy (DOE). The purpose of the analysis is twofold. The first is to quantify relative attractiveness of commute modes between the two locations, using a perspective that includes travel time, energy and cost, while providing an equity lens to compare commute options between privately owned vehicles and pooled transportation options. The second objective is to apply MEP in a specific origin-destination (O-D) scenario, whereas previously it has been used primarily as an aggregate metropolitan-wide statistical measure. In so doing, parameters in MEP are further customized and the methodology is refined to account for unique aspects of this case study. Four commute options between the neighborhood and the industry employment based are analyzed: drive alone option, public transit express bus (historical), public transit normal route (current), and a proposed shuttle specific to the O-D pair. This analysis identified issues applying MEP that required further customization: (1) deprecation functions customized to modes other than driving, (2) accounting for first-mile last-mile travel times with transit, (3) accounting for transit frequency without resorting to full simulation. The results provide quantitative insights on the employment accessibility between these two locations, both across modes, and as equity of job accessibility for those who can and cannot operate a personal vehicle.
In this work, I explore the concept of quantization as a mapping from classical phase space functions to quantum operators. I discuss the early history of this notion of quantization with emphasis on the works of Schrödinger and Dirac, and how quantization fit into their overall understanding of quantum theory in the 1920's. Dirac, in particular, proposed a quantization map which should satisfy certain properties, including the property that quantum commutators should be related to classical Poisson brackets in a particular way. However, in 1946, Groenewold proved that Dirac's mapping was inconsistent, making the problem of defining a rigorous quantization map more elusive than originally expected. This result, known as the Groenewold-Van Hove theorem, is not often discussed in physics texts, but here I will give an account of the theorem and what it means for potential ``corrections” to Dirac's scheme. Other proposals for quantization have arisen over the years, the first major one being that of Weyl in 1927, which was later developed by many, including Groenewold, and which has since become known as Weyl Quantization in the mathematical literature. Another, known as Geometric Quantization, formulates quantization in differential-geometric terms by appealing to the character of classical phase spaces as symplectic manifolds; this approach began with the work of Souriau, Kostant, and Kirillov in the 1960's. I will describe these proposals for quantization and comment on their relation to Dirac's original program. Along the way, the problem of operator ordering and of quantizing in curvilinear coordinates will be described, since these are natural questions that immediately present themselves when thinking about quantization.
We present a strategy for mapping the dynamics of a fermionic quantum system to a set of classical dynamical variables. The approach is based on imposing the correspondence relation between the commutator and the Poisson bracket, preserving Heisenberg's equation of motion for one-body operators. In order to accommodate the effect of two-body terms, we further impose quantization on the spin-dependent occupation numbers in the classical equations of motion, with a parameter that is determined self-consistently. Expectation values for observables are taken with respect to an initial quasiclassical distribution that respects the original quantization of the occupation numbers. The proposed classical map becomes complete under the evolution of quadratic Hamiltonians and is extended for all even order observables. We show that the map provides an accurate description of the dynamics for an interacting quantum impurity model in the coulomb blockade regime, at both low and high temperatures. In conclusion, the numerical results are aided by a novel importance sampling scheme that employs a reference system to reduce significantly the sampling effort required to converge the classical calculations.
In this work, we introduce the notion of combinatorial gauge symmetry—a local transformation that includes single spin rotations plus permutations of spins (or swaps of their quantum states)—that preserve the commutation and anticommutation relations among the spins. We show that Hamiltonians with simple two-body interactions contain this symmetry if the coupling matrix is a Hadamard matrix, with the combinatorial gauge symmetry being associated with the automorphism of these matrices with respect to monomial transformations. Armed with this symmetry, we address the physical problem of how to build quantum spin liquids with physically accessible interactions. In addition to its intrinsic physical significance, the problem is also tied to that of how to build topological qubits.
We derive a Kubo-like formula for the thermal Hall conductance of a 2d lattice systems which is free from ambiguities associated with the definition of energy magnetization. We use it to define a relative topological invariant of gapped 2d lattice systems at zero temperature. Up to a numerical factor, it can be identified with the difference of chiral central charges for the corresponding edge modes. This establishes the bulk-boundary correspondence for the chiral central charge. Here, we also show that for any local commuting projector Hamiltonian, the relative chiral central charge vanishes, while for free fermionic systems, it is related to the zero-temperature electric Hall conductance via the Wiedemann-Franz law.
Results are compared for comfort and environmental studies taken in conjunction with a STOL program. Data were taken on flights of four different airlines, each flying different aircraft. Two of the lines are classified as commuter airlines flying between relatively close destinations. The aircraft involved are: the De Havilland Twin Otter, a Canadian aircraft; the French Nord 262; the Beechcraft 99 Airliner and the Sikorsky S-61 helicopter, both American.
The invention disclosed in this document is a brushless DC motor including a housing having an end cap secured thereto. The housing encloses a rotor, a stator and a rotationally displaceable commutation board having 5 sensors secured thereon and spaced around the periphery of the rotor. An external rotational force is applied to the commutation board for displacement of the sensors to various positions whereby varying feedback signals are generated by the positioning of the sensors relative to the rotating rotor. The commutation board is secured in a fixed position in response to feedback signals indicative of optimum sensor position being determined. The rotation of the commutation board and the securing of the sensors in the desired fixed position is accomplished without requiring the removal of the 5 end cap and with the DC motor operating.
A brushless DC motor including a housing having an end cap secured thereto. The housing encloses a rotor. a stator and a rotationally displaceable commutation board having sensors secured thereon and spaced around the periphery of the rotor. An external rotational force is applied to the commutation board for displacement of the sensors to various positions whereby varying feedback signals are generated by the positioning of the sensors relative to the rotating rotor. The commutation board is secured in a fixed position in response to feedback signals indicative of optimum sensor position being determined. The rotation of the commutation board and the securing of the sensors in the desired fixed position is accomplished without requiring the removal of the end cap and with the DC motor operating.
Information on commuter airline trends and aircraft developments is provided to upgrade the preliminary findings of a NASA-formed small transport aircraft technology (STAT) team, established to determine whether the agency's research and development programs could help commuter aircraft manufacturers solve technical problems related to passenger acceptance and use of 19- to 50-passenger aircraft. The results and conclusions of the full set of completed STAT studies are presented. These studies were performed by five airplane manufacturers, five engine manufacturers, and two propeller manufacturers. Those portions of NASA's overall aeronautics research and development programs which are applicable to commuter aircraft design are summarized. Areas of technology that might beneficially be expanded or initiated to aid the US commuter aircraft manufacturers in the evolution of improved aircraft for the market are suggested.
The short-haul service abandoned by the trunk and local airlines is being picked up by the commuter airlines using small turboprop-powered aircraft. Most of the existing small transport aircraft currently available represent a relatively old technology level. However, several manufacturers have initiated the development of new or improved commuter transport aircraft. These aircraft are relatively conservative in terms of technology. An examination is conducted of advanced technology to identify those technologies that, if developed, would provide the largest improvements for future generations of these aircraft. Attention is given to commuter aircraft operating cost, aerodynamics, structures and materials, propulsion, aircraft systems, and technology integration. It is found that advanced technology can improve future commuter aircraft and that the largest of these improvements will come from the synergistic combination of technological advances in all of the aircraft disciplines. The most important goals are related to improved fuel efficiency and increased aircraft productivity.