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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.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

On the essential spectrum of certain non-commutative oscillators

We show here that the spectrum of the family of non-commutative harmonic oscillators Q{sub (α,β)}{sup w}(x,D) for α,β∈R{sub +} in the range αβ = 1 is [0, +∞) and is entirely essential spectrum. The previous existing results concern the case αβ > 1 (case in which Q{sub (α,β)}{sup w}(x,D) is globally elliptic with a discrete spectrum whose qualitative properties are being extensively studied), and ours therefore extend the picture to the range of parameters αβ ⩾ 1.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Group theoretical construction of planar noncommutative phase spaces

Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally abelian extended planar absolute time Lie groups. Through these constructions the coordinates of the phase spaces do not commute due to the presence of naturally introduced fields giving rise to minimal couplings. By symplectic realizations methods, physical interpretations of generators coming from the obtained structures are given.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Trace inequalities for products of positive definite matrices

It is shown that for positive definite matrices A and B the inequality ‖A{sup p}B{sup q} + B{sup p}A{sup q}‖{sub 2} ⩽ ‖A{sup p}B{sup q} + A{sup q}B{sup p}‖{sub 2} holds for all positive real number p and q for which p/(p + q) is in [1/4, 3/4]. This is a significant improvement on a recent result of Hayajneh and Kittaneh [“Lieb-Thirring trace inequalities and a question of Bourin,” J. Math. Phys. 54, 033504 (2013)].

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Curvature and geometric modules of noncommutative spheres and tori

When considered as submanifolds of Euclidean space, the Riemannian geometry of the round sphere and the Clifford torus may be formulated in terms of Poisson algebraic expressions involving the embedding coordinates, and a central object is the projection operator, projecting tangent vectors in the ambient space onto the tangent space of the submanifold. In this note, we point out that there exist noncommutative analogues of these projection operators, which implies a very natural definition of noncommutative tangent spaces as particular projective modules. These modules carry an induced connection from Euclidean space, and we compute its scalar curvature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Construction of the noncommutative complex ball

We describe the construction of the noncommutative complex ball whose commutative analog is the Hermitian symmetric space D = SU(m, 1)/U(m), with the method of coherent state quantization. In the commutative limit, we obtain the standard manifold. We also consider a quantum field theory model on the noncommutative manifold.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Non-geometric fluxes, quasi-Hopf twist deformations, and nonassociative quantum mechanics

We analyse the symmetries underlying nonassociative deformations of geometry in non-geometric R-flux compactifications which arise via T-duality from closed strings with constant geometric fluxes. Starting from the non-abelian Lie algebra of translations and Bopp shifts in phase space, together with a suitable cochain twist, we construct the quasi-Hopf algebra of symmetries that deforms the algebra of functions and the exterior differential calculus in the phase space description of nonassociative R-space. In this setting, nonassociativity is characterised by the associator 3-cocycle which controls non-coassociativity of the quasi-Hopf algebra. We use abelian 2-cocycle twists to construct maps between the dynamical nonassociative star product and a family of associative star products parametrized by constant momentum surfaces in phase space. We define a suitable integration on these nonassociative spaces and find that the usual cyclicity of associative noncommutative deformations is replaced by weaker notions of 2-cyclicity and 3-cyclicity. Using this star product quantization on phase space together with 3-cyclicity, we formulate a consistent version of nonassociative quantum mechanics, in which we calculate the expectation values of area and volume operators, and find coarse-graining of the string background due to the R-flux.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

On variational definition of quantum entropy

Entropy of distribution P can be defined in at least three different ways: 1) as the expectation of the Kullback-Leibler (KL) divergence of P from elementary δ-measures (in this case, it is interpreted as expected surprise); 2) as a negative KL-divergence of some reference measure ν from the probability measure P; 3) as the supremum of Shannon’s mutual information taken over all channels such that P is the output probability, in which case it is dual of some transportation problem. In classical (i.e. commutative) probability, all three definitions lead to the same quantity, providing only different interpretations of entropy. In non-commutative (i.e. quantum) probability, however, these definitions are not equivalent. In particular, the third definition, where the supremum is taken over all entanglements of two quantum systems with P being the output state, leads to the quantity that can be twice the von Neumann entropy. It was proposed originally by V. Belavkin and Ohya [1] and called the proper quantum entropy, because it allows one to define quantum conditional entropy that is always non-negative. Here we extend these ideas to define also quantum counterpart of proper cross-entropy and cross-information. We also show inequality for the values of classical and quantum information.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

The Kastler-Kalau-Walze type theorem for six-dimensional manifolds with boundary

In this paper, we define lower dimensional volumes of spin manifolds with boundary. We compute the lower dimensional volume V ol{sub 6}{sup (1,3)} for 6-dimensional spin manifolds with boundary and derive the gravity on boundary from the noncommutative residue associated with Dirac operators. For 6-dimensional manifolds with boundary, we also get a Kastler-Kalau-Walze type theorem for a general fourth order operator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Natural discretization in noncommutative field theory

A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Curved noncommutative tori as Leibniz quantum compact metric spaces

We prove that curved noncommutative tori are Leibniz quantum compact metric spaces and that they form a continuous family over the group of invertible matrices with entries in the image of the quantum tori for the conjugation by modular conjugation operator in the regular representation, when this group is endowed with a natural length function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

On supermatrix models, Poisson geometry, and noncommutative supersymmetric gauge theories

We construct a new supermatrix model which represents a manifestly supersymmetric noncommutative regularisation of the UOSp(2|1) supersymmetric Schwinger model on the supersphere. Our construction is much simpler than those already existing in the literature and it was found by using Poisson geometry in a substantial way.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Powers of sets in free groups

We prove that |A{sup n}|{>=}c{sub n}{center_dot}|A|{sup [(n+1)/2]} for any finite subset A of a free group if A contains at least two noncommuting elements, where the c{sub n}>0 are constants not depending on A. Simple examples show that the order of these estimates is best possible for each n>0. Bibliography: 5 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Reversibility conditions for quantum channels and their applications

Conditions for a quantum channel (noncommutative Markov operator) to be reversible with respect to complete families of quantum states with bounded rank are obtained. A description of all quantum channels reversible with respect to a given (orthogonal or nonorthogonal) complete family of pure states is given. Some applications in quantum information theory are considered. Bibliography: 20 titles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Noncommutative reciprocity laws on algebraic surfaces: the case of tame ramification

We prove noncommutative reciprocity laws on an algebraic surface defined over a perfect field. These reciprocity laws establish that some central extensions of globally constructed groups split over certain subgroups constructed by points or projective curves on a surface. For a two-dimensional local field with a last finite residue field, the local central extension which is constructed is isomorphic to the central extension which comes from the case of tame ramification of the Abelian two-dimensional local Langlands correspondence suggested by Kapranov. Bibliography: 9 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Constraints on noncommutative spectral action from Gravity Probe B and torsion balance experiments

Noncommutative spectral geometry offers a purely geometric explanation for the standard model of strong and electroweak interactions, including a geometric explanation for the origin of the Higgs field. Within this framework, the gravitational, the electroweak and the strong forces are all described as purely gravitational forces on a unified noncommutative space-time. In this study, we infer a constraint on one of the three free parameters of the model, namely the one characterising the coupling constants at unification, by linearising the field equations in the limit of weak gravitational fields generated by a rotating gravitational source, and by making use of recent experimental data. In particular, using data obtained by Gravity Probe B, we set a lower bound on the Weyl term appearing in the noncommutative spectral action, namely β∼>10{sup −6}m{sup −1}. This constraint becomes stronger once we use results from torsion balance experiments, leading to β∼>10{sup 4}m{sup −1}. The latter is much stronger than any constraint imposed so far to curvature squared terms.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

CMB statistical anisotropy from noncommutative gravitational waves

Primordial statistical anisotropy is a key indicator to investigate early Universe models and has been probed by the cosmic microwave background (CMB) anisotropies. In this paper, we examine tensor-mode CMB fluctuations generated from anisotropic gravitational waves, parametrised by P{sub h}(k) = P{sub h}{sup (0)}(k) [ 1 + ∑{sub LM} f{sub L}(k) g{sub LM} Y{sub LM} ( k-circumflex )], where P{sub h}{sup (0)}(k) is the usual scale-invariant power spectrum. Such anisotropic tensor fluctuations may arise from an inflationary model with noncommutativity of fields. It is verified that in this model, an isotropic component and a quadrupole asymmetry with f{sub 0}(k) = f{sub 2}(k) ∝ k{sup -2} are created and hence highly red-tilted off-diagonal components arise in the CMB power spectra, namely ℓ{sub 2} = ℓ{sub 1} ± 2 in TT, TE, EE and BB, and ℓ{sub 2} = ℓ{sub 1} ± 1 in TB and EB. We find that B-mode polarisation is more sensitive to such signals than temperature and E-mode polarisation due to the smallness of large-scale cosmic variance and we can potentially measure g{sub 00} = 30 and g{sub 2M} = 58 at 68% CL in a cosmic-variance-limited experiment. Such a level of signal may be measured in a PRISM like experiment, while the instrumental noise contaminates it in the Planck experiment. These results imply that it is impossible to measure the noncommutative parameter if it is small enough for the perturbative treatment to be valid. Our formalism and methodology for dealing with the CMB tensor statistical anisotropy are general and straightforwardly applicable to other early Universe models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Shadow of noncommutative geometry inspired black hole

In this paper, the shadow casted by the rotating black hole inspired by noncommutative geometry is investigated. In addition to the dimensionless spin parameter a/M{sub 0} with M{sub 0} black hole mass and inclination angle i, the dimensionless noncommutative parameter √θ/M{sub 0} is also found to affect the shape of the black hole shadow. The result shows that the size of the shadow slightly decreases with the parameter √θ/M{sub 0}, while the distortion increases with it. Compared to the Kerr black hole, the parameter √θ/M{sub 0} increases the deformation of the shadow. This may offer a way to distinguish noncommutative geometry inspired black hole from Kerr one via astronomical instruments in the near future.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Spin Hall effect on a noncommutative space

We study the spin-orbital interaction and the spin Hall effect of an electron moving on a noncommutative space under the influence of a vector potential A(vector sign). On a noncommutative space, we find that the commutator between the vector potential A(vector sign) and the electric potential V{sub 1}(r(vector sign)) of the lattice induces a new term, which can be treated as an effective electric field, and the spin Hall conductivity obtains some correction. On a noncommutative space, the spin current and spin Hall conductivity have distinct values in different directions, and depend explicitly on the noncommutative parameter. Once this spin Hall conductivity in different directions can be measured experimentally with a high level of accuracy, the data can then be used to impose bounds on the value of the space noncommutativity parameter. We have also defined a new parameter, {sigma}={rho}{theta} ({rho} is the electron concentration, {theta} is the noncommutativity parameter), which can be measured experimentally. Our approach is based on the Foldy-Wouthuysen transformation, which gives a general Hamiltonian of a nonrelativistic electron moving on a noncommutative space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗