14,291 research outputs found
Entanglement production in quantum decision making
The quantum decision theory introduced recently is formulated as a quantum
theory of measurement. It describes prospect states represented by complex
vectors of a Hilbert space over a prospect lattice. The prospect operators,
acting in this space, form an involutive bijective algebra. A measure is
defined for quantifying the entanglement produced by the action of prospect
operators. This measure characterizes the level of complexity of prospects
involved in decision making. An explicit expression is found for the maximal
entanglement produced by the operators of multimode prospects.Comment: Latex file, 7 page
Debye Potentials for Maxwell and Dirac Fields from a Generalisation of the Killing-Yano Equation
By using conformal Killing-Yano tensors, and their generalisations, we obtain
scalar potentials for both the source-free Maxwell and massless Dirac
equations. For each of these equations we construct, from conformal
Killing-Yano tensors, symmetry operators that map any solution to another.Comment: 35 pages, plain Te
The Inverse Shapley Value Problem
For a weighted voting scheme used by voters to choose between two
candidates, the \emph{Shapley-Shubik Indices} (or {\em Shapley values}) of
provide a measure of how much control each voter can exert over the overall
outcome of the vote. Shapley-Shubik indices were introduced by Lloyd Shapley
and Martin Shubik in 1954 \cite{SS54} and are widely studied in social choice
theory as a measure of the "influence" of voters. The \emph{Inverse Shapley
Value Problem} is the problem of designing a weighted voting scheme which
(approximately) achieves a desired input vector of values for the
Shapley-Shubik indices. Despite much interest in this problem no provably
correct and efficient algorithm was known prior to our work.
We give the first efficient algorithm with provable performance guarantees
for the Inverse Shapley Value Problem. For any constant \eps > 0 our
algorithm runs in fixed poly time (the degree of the polynomial is
independent of \eps) and has the following performance guarantee: given as
input a vector of desired Shapley values, if any "reasonable" weighted voting
scheme (roughly, one in which the threshold is not too skewed) approximately
matches the desired vector of values to within some small error, then our
algorithm explicitly outputs a weighted voting scheme that achieves this vector
of Shapley values to within error \eps. If there is a "reasonable" voting
scheme in which all voting weights are integers at most \poly(n) that
approximately achieves the desired Shapley values, then our algorithm runs in
time \poly(n) and outputs a weighted voting scheme that achieves the target
vector of Shapley values to within error $\eps=n^{-1/8}.
Evidence of Skyrmion excitations about in n-Modulation Doped Single Quantum Wells by Inter-band Optical Transmission
We observe a dramatic reduction in the degree of spin-polarization of a
two-dimensional electron gas in a magnetic field when the Fermi energy moves
off the mid-point of the spin-gap of the lowest Landau level, . This
rapid decay of spin alignment to an unpolarized state occurs over small changes
to both higher and lower magnetic field. The degree of electron spin
polarization as a function of is measured through the magneto-absorption
spectra which distinguish the occupancy of the two electron spin states. The
data provide experimental evidence for the presence of Skyrmion excitations
where exchange energy dominates Zeeman energy in the integer quantum Hall
regime at
The Origin of the Electromagnetic Interaction in Einstein's Unified Field Theory with Sources
Einstein's unified field theory is extended by the addition of matter terms
in the form of a symmetric energy tensor and of two conserved currents. From
the field equations and from the conservation identities emerges the picture of
a gravoelectrodynamics in a dynamically polarizable Riemannian continuum.
Through an approximate calculation exploiting this dynamical polarizability it
is argued that ordinary electromagnetism may be contained in the theory.Comment: 8 pages. Misprint in eq. 15 correcte
A comparative DFT study of electronic properties of 2H-, 4H- and 6H-SiC(0001) and SiC(000-1) clean surfaces: Significance of the surface Stark effect
Electric field, uniform within the slab, emerging due to Fermi level pinning
at its both sides is analyzed using DFT simulations of the SiC surface slabs of
different thickness. It is shown that for thicker slab the field is nonuniform
and this fact is related to the surface state charge. Using the electron
density and potential profiles it is proved that for high precision simulations
it is necessary to take into account enough number of the Si-C layers. We show
that using 12 diatomic layers leads to satisfactory results. It is also
demonstrated that the change of the opposite side slab termination, both by
different type of atoms or by their location, can be used to adjust electric
field within the slab, creating a tool for simulation of surface properties,
depending on the doping in the bulk of semiconductor. Using these simulations
it was found that, depending on the electric field, the energy of the surface
states changes in a different way than energy of the bulk states. This
criterion can be used to distinguish Shockley and Tamm surface states. The
electronic properties, i.e. energy and type of surface states of the three
clean surfaces: 2H-, 4H-, 6H-SiC(0001), and SiC() are analyzed and
compared using field dependent DFT simulations.Comment: 18 pages, 10 figures, 4 table
NMR Chemical Shifts of Trace Impurities: Common Laboratory Solvents, Organics, and Gases in Deuterated Solvents Relevant to the Organometallic Chemist
Tables of ^1H and ^(13)C NMR chemical shifts have been compiled for common organic compounds often used as reagents or found as products or contaminants in deuterated organic solvents. Building upon the work of Gottlieb, Kotlyar, and Nudelman in the Journal of Organic Chemistry, signals for common impurities are now reported in additional NMR solvents (tetrahydrofuran-d_8, toluene-d_8, dichloromethane-d_2, chlorobenzene-d_5, and 2,2,2-trifluoroethanol-d_3) which are frequently used in organometallic laboratories. Chemical shifts for other organics which are often used as reagents or internal standards or are found as products in organometallic chemistry are also reported for all the listed solvents
CR Structures and Asymptotically Flat Space-Times
We discuss the unique existence, arising by analogy to that in algebraically
special space-times, of a CR structure realized on null infinity for any
asymptotically flat Einstein or Einstein-Maxwell space-time.Comment: 6 page
Expanding perfect fluid generalizations of the C-metric
We reexamine Petrov type D gravitational fields generated by a perfect fluid
with spatially homogeneous energy density and in which the flow lines form a
timelike non-shearing and non-rotating congruence. It is shown that the
anisotropic such spacetimes, which comprise the vacuum C-metric as a limit
case, can have \emph{non-zero} expansion, contrary to the conclusion in the
original investigation by Barnes (Gen. Rel. Grav. 4, 105 (1973)). This class
consists of cosmological models with generically one and at most two Killing
vectors. We construct their line element and discuss some important properties.
The methods used in this investigation incite to deduce testable criteria
regarding shearfree normality and staticity op Petrov type spacetimes in
general, which we add in an appendix.Comment: 16 pages, extended and amended versio
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