10,009 research outputs found
Measuring the foaminess of space-time with gravity-wave interferometers
By analyzing a gedanken experiment designed to measure the distance
between two spatially separated points, we find that this distance cannot be
measured with uncertainty less than , considerably larger than
the Planck scale (or the string scale in string theories), the
conventional wisdom uncertainty in distance measurements. This limitation to
space-time measurements is interpreted as resulting from quantum fluctuations
of space-time itself. Thus, at very short distance scales, space-time is
"foamy." This intrinsic foaminess of space-time provides another source of
noise in the interferometers. The LIGO/VIRGO and LISA generations of
gravity-wave interferometers, through future refinements, are expected to reach
displacement noise levels low enough to test our proposed degree of foaminess
in the structure of space-time. We also point out a simple connection to the
holographic principle which asserts that the number of degrees of freedom of a
region of space is bounded by the area of the region in Planck units.Comment: 15 pages, TeX, A simple connection to the holographic principle is
added, minor changes in the text and abstract, and some changes in the
References; this new version will appear in the third "Haller" issue in
Foundations of Physic
An application of neutrix calculus to quantum field theory
Neutrices are additive groups of negligible functions that do not contain any
constants except 0. Their calculus was developed by van der Corput and Hadamard
in connection with asymptotic series and divergent integrals. We apply neutrix
calculus to quantum field theory, obtaining finite renormalizations in the loop
calculations. For renormalizable quantum field theories, we recover all the
usual physically observable results. One possible advantage of the neutrix
framework is that effective field theories can be accommodated. Quantum gravity
theories appear to be more manageable.Comment: LateX, 19 page
Projective Geometry and -Symmetric Dirac Hamiltonian
The -dimensional (generalized) Dirac equation is shown to have the
same form as the equation expressing the condition that a given point lies on a
given line in 3-dimensional projective space. The resulting Hamiltonian with a
mass term is not Hermitian, but is invariant under the combined
transformation of parity reflection and time reversal . When
the symmetry is unbroken, the energy spectrum of the free spin- theory is real, with an appropriately shifted mass.Comment: 7 pages, LaTeX; version accepted for publication in Phys. Lett. B;
revised version incorporates useful suggestions from an anonymous refere
Regular graphs with maximal energy per vertex
We study the energy per vertex in regular graphs. For every k, we give an
upper bound for the energy per vertex of a k-regular graph, and show that a
graph attains the upper bound if and only if it is the disjoint union of
incidence graphs of projective planes of order k-1 or, in case k=2, the
disjoint union of triangles and hexagons. For every k, we also construct
k-regular subgraphs of incidence graphs of projective planes for which the
energy per vertex is close to the upper bound. In this way, we show that this
upper bound is asymptotically tight
Distance-regular graphs
This is a survey of distance-regular graphs. We present an introduction to
distance-regular graphs for the reader who is unfamiliar with the subject, and
then give an overview of some developments in the area of distance-regular
graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A.,
Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page
Graphs with many valencies and few eigenvalues
Dom de Caen posed the question whether connected graphs with three distinct
eigenvalues have at most three distinct valencies. We do not answer this
question, but instead construct connected graphs with four and five distinct
eigenvalues and arbitrarily many distinct valencies. The graphs with four
distinct eigenvalues come from regular two-graphs. As a side result, we
characterize the disconnected graphs and the graphs with three distinct
eigenvalues in the switching class of a regular two-graph
Modeling low order aberrations in laser guide star adaptive optics systems
When using a laser guide star (LGS) adaptive optics (AO) system, quasi-static aberrations are observed between the measured wavefronts from the LGS wavefront sensor (WFS) and the natural guide star (NGS) WFS. These LGS aberrations, which can be as much as 1200 nm RMS on the Keck II LGS AO system, arise due to the finite height and structure of the sodium layer. The LGS aberrations vary significantly between nights due to the difference in sodium structure. In this paper, we successfully model these LGS aberrations for the Keck II LGS AO system. We use this model to characterize the LGS aberrations as a function of pupil angle, elevation, sodium structure, uplink tip/tilt error, detector field of view, the number of detector pixels, and seeing. We also employ the model to estimate the LGS aberrations for the Palomar LGS AO system, the planned Keck I and the Thirty Meter Telescope (TMT) LGS AO systems. The LGS aberrations increase with increasing telescope diameter, but are reduced by central projection of the laser compared to side projection
Tight Noise Thresholds for Quantum Computation with Perfect Stabilizer Operations
We study how much noise can be tolerated by a universal gate set before it
loses its quantum-computational power. Specifically we look at circuits with
perfect stabilizer operations in addition to imperfect non-stabilizer gates. We
prove that for all unitary single-qubit gates there exists a tight depolarizing
noise threshold that determines whether the gate enables universal quantum
computation or if the gate can be simulated by a mixture of Clifford gates.
This exact threshold is determined by the Clifford polytope spanned by the 24
single-qubit Clifford gates. The result is in contrast to the situation wherein
non-stabilizer qubit states are used; the thresholds in that case are not
currently known to be tight.Comment: 4 pages, 2 figure
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