SEARCH · Search NASA
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
This article discusses the structure of cyclic semirings with nonidempotent noncommutative addition. Also given are some general results on cyclic semirings with noncommutative addition.
In this paper, we prove a criterion for elementary equivalence of stable linear groups over commutative local rings with invertible two.
We characterize linear transformations on matrices over commutative antinegative semirings that are monotone with respect to minus, star, and sharp partial orders.
The paper presents new results on varieties of commutative metabelian algebras over a field of zero characteristic. We study the structure of the multilinear part of the variety of all commutative metabelian algebras as a module of the symmetric group. Two almost nilpotent varieties are introduced and studied in this class of algebras. We prove the nonexistence of other almost nilpotent commutative metabelian varieties of subexponential growth.
We give an interpretation of the magnetic Schrödinger operator in terms of noncommutative geometry. In particular, spectral properties of this operator are reformulated in terms of C*-algebras. Using this reformulation, one can employ the machinery of noncommutative geometry, such as Hochschild cohomology, to study the properties of the magnetic Schrödinger operator. We show how this idea can be applied to the integer quantum Hall effect.
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.
We investigated the thermodynamic properties of graphene in a noncommutative phase–space in the presence of a constant magnetic field. In particular, we determined the behaviour of the main thermodynamical functions: the Helmholtz free energy, the mean energy, the entropy and the specific heat. The high temperature limit is worked out and the thermodynamic quantities, such as mean energy and specific heat, exhibit the same features as the commutative case. Possible connections with the results already established in the literature are discussed briefly.
The matching method is employed to analytically investigate the properties of holographic superconductors in higher dimensions in the framework of power Maxwell electrodynamics taking into account the effects of spacetime noncommutativity. The relationship between the critical temperature and the charge density and the value of the condensation operator is obtained first. The Meissner like effect is then studied. The analysis indicates that larger values of the noncommutative parameter and the parameter q appearing in the power Maxwell theory make the condensate difficult to form. The critical magnetic field however increases with increase in the noncommutative parameter θ.
We consider a noncommutative (NC) inflationary model with a homogeneous scalar field minimally coupled to gravity. The particular NC inflationary setting herein proposed, produces entirely new consequences as summarized in what follows. We first analyze the free field case and subsequently examine the situation where the scalar field is subjected to a polynomial and exponential potentials. We propose to use a canonical deformation between momenta, in a spatially flat Friedmann–Lemaî tre–Robertson–Walker (FLRW) universe, and while the Friedmann equation (Hamiltonian constraint) remains unaffected the Friedmann acceleration equation (and thus the Klein–Gordon equation) is modified by an extra term linear in the NC parameter. This concrete noncommutativity on the momenta allows interesting dynamics that other NC models seem not to allow. Let us be more precise. This extra term behaves as the sole explicit pressure that under the right circumstances implies a period of accelerated expansion of the universe. We find that in the absence of the scalar field potential, and in contrast with the commutative case, in which the scale factor always decelerates, we obtain an inflationary phase for small negative values of the NC parameter. Subsequently, the period of accelerated expansion is smoothly replaced by an appropriate deceleration phase providing an interesting model regarding the graceful exit problem in inflationary models. This last property is present either in the free field case or under the influence of the scalar field potentials considered here. Moreover, in the case of the free scalar field, we show that not only the horizon problem is solved but also there is some resemblance between the evolution equation of the scale factor associated to our model and that for the R{sup 2} (Starobinsky) inflationary model. Therefore, our herein NC model not only can be taken as an appropriate scenario to get a successful kinetic inflation, but also is a convenient setting to obtain inflationary universe possessing the graceful exit when scalar field potentials are present.
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 the connection between quantum field theories on flat noncommutative space(-times) in Euclidean and Lorentzian signature is studied for the case that time is still commutative. By making use of the algebraic framework of quantum field theory and an analytic continuation of the symmetry groups which are compatible with the structure of Moyal space, a general correspondence between field theories on Euclidean space satisfying a time zero condition and quantum field theories on Moyal Minkowski space is presented ('Wick rotation'). It is then shown that field theories transferred to Moyal space(-time) by Rieffel deformation and warped convolution fit into this framework, and that the processes of Wick rotation and deformation commute.
We propose that there exist generalized Seiberg-Witten equations in the Liouville conformal field theory, which allow the computation of correlation functions from the resolution of certain Ward identities. These identities involve a multivalued spin one chiral field, which is built from the energy-momentum tensor. We solve the Ward identities perturbatively in an expansion around the heavy asymptotic limit, and check that the first two terms of the Liouville three-point function agree with the known result of Dorn, Otto, Zamolodchikov, and Zamolodchikov. We argue that such calculations can be interpreted in terms of the geometry of non-commutative spectral curves.
States in algebraic quantum field theory 'typically' establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V{sub A} and V{sub B}, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V{sub A} and V{sub B} and the set {l_brace}C, C{sup Up-Tack }{r_brace} screens off the correlation between A and B.
The theory of α*-cohomology is studied thoroughly and it is shown that in each cohomology class there exists a unique 2-cocycle, the harmonic form, which generates a particular Groenewold-Moyal star product. This leads to an algebraic classification of translation-invariant non-commutative structures and shows that any general translation-invariant non-commutative quantum field theory is physically equivalent to a Groenewold-Moyal non-commutative quantum field theory.
Quantum Mechanics, as a mini-superspace of Field Theory has been assumed to provide physically relevant information on quantum processes in Field Theory. In the case of Quantum Gravity this would imply using Cosmological models to investigate quantum processes at distances of the order of the Planck scale. However because of the Stone-von Neuman Theorem, it is well known that quantization of Cosmological models by the Wheeler-DeWitt procedure in the context of a Heisenberg-Weyl group with piecewise continuous parameters leads irremediably to a volume singularity. In order to avoid this information catastrophe it has been suggested recently the need to introduce in an effective theory of the quantization some form of reticulation in 3-space. On the other hand, since in the geometry of the General Relativistic formulation of Gravitation space can not be visualized as some underlying static manifold in which the physical system evolves, it would be interesting to investigate whether the effective reticulation which removes the singularity in such simple cosmologies as the Bianchi models has a dynamical origin manifested by a noncommutativity of the generators of the Heisenberg-Weyl algebra, as would be expected from an operational point of view at the Planck length scale.