48,745 research outputs found
From Topology to Generalised Dimensional Reduction
In the usual procedure for toroidal Kaluza-Klein reduction, all the
higher-dimensional fields are taken to be independent of the coordinates on the
internal space. It has recently been observed that a generalisation of this
procedure is possible, which gives rise to lower-dimensional ``massive''
supergravities. The generalised reduction involves allowing gauge potentials in
the higher dimension to have an additional linear dependence on the toroidal
coordinates. In this paper, we show that a much wider class of generalised
reductions is possible, in which higher-dimensional potentials have additional
terms involving differential forms on the internal manifold whose exterior
derivatives yield representatives of certain of its cohomology classes. We
consider various examples, including the generalised reduction of M-theory and
type II strings on K3, Calabi-Yau and 7-dimensional Joyce manifolds. The
resulting massive supergravities support domain-wall solutions that arise by
the vertical dimensional reduction of higher-dimensional solitonic p-branes and
intersecting p-branes.Comment: Latex, 24 pages, no figures, typo corrected, reference added and
discussion of duality extende
Computing the Girth of a Planar Graph in Linear Time
The girth of a graph is the minimum weight of all simple cycles of the graph.
We study the problem of determining the girth of an n-node unweighted
undirected planar graph. The first non-trivial algorithm for the problem, given
by Djidjev, runs in O(n^{5/4} log n) time. Chalermsook, Fakcharoenphol, and
Nanongkai reduced the running time to O(n log^2 n). Weimann and Yuster further
reduced the running time to O(n log n). In this paper, we solve the problem in
O(n) time.Comment: 20 pages, 7 figures, accepted to SIAM Journal on Computin
An accretion model for the growth of the central black hole associated with ionization instability in quasars
A possible accretion model associated with the ionization instability of
quasar disks is proposed to address the growth of the central black hole
harbored in the host galaxy.The mass ratio between black hole and its host
galactic bulge is a nature consequence of our model.Comment: submitted to ApJ, 15 page
An Optimal Algorithm for the Maximum-Density Segment Problem
We address a fundamental problem arising from analysis of biomolecular
sequences. The input consists of two numbers and and a
sequence of number pairs with . Let {\em segment}
of be the consecutive subsequence of between indices and
. The {\em density} of is
. The {\em maximum-density
segment problem} is to find a maximum-density segment over all segments
with . The best
previously known algorithm for the problem, due to Goldwasser, Kao, and Lu,
runs in time. In the present paper, we solve
the problem in O(n) time. Our approach bypasses the complicated {\em right-skew
decomposition}, introduced by Lin, Jiang, and Chao. As a result, our algorithm
has the capability to process the input sequence in an online manner, which is
an important feature for dealing with genome-scale sequences. Moreover, for a
type of input sequences representable in space, we show how to
exploit the sparsity of and solve the maximum-density segment problem for
in time.Comment: 15 pages, 12 figures, an early version of this paper was presented at
11th Annual European Symposium on Algorithms (ESA 2003), Budapest, Hungary,
September 15-20, 200
Subgap states in dirty superconductors and their effect on dephasing in Josephson qubits
We present a theory of the subgap tails of the density of states in a
diffusive superconductor containing magnetic impurities. We show that the
subgap tails have two contributions: one arising from mesoscopic gap
fluctuations, previously discussed by Lamacraft and Simons, and the other
associated to the long-wave fluctuations of the concentration of magnetic
impurities. We study the latter both in small superconducting grains and in
bulk systems [], and establish the dimensionless parameter that
controls which of the two contributions dominates the subgap tails. We observe
that these contributions are related to each other by dimensional reduction. We
apply the theory to estimate the effects of a weak concentration of magnetic
impurities [] on the phase coherence of Josephson
qubits. We find that at these typical concentrations, magnetic impurities are
relevant for the dephasing in large qubits, designed around a
scale, where they limit the quality factor to be .Comment: 13 pages, 1 figur
Structure and spatial distribution of Ge nanocrystals subjected to fast neutron irradiation
The influence of fast neutron irradiation on the structure and spatial
distribution of Ge nanocrystals (NC) embedded in an amorphous SiO2 matrix has
been studied. The investigation was conducted by means of laser Raman
Scattering (RS), High Resolution Transmission Electron Microscopy (HR-TEM) and
X-ray photoelectron spectroscopy (XPS). The irradiation of NC-Ge samples by a
high dose of fast neutrons lead to a partial destruction of the nanocrystals.
Full reconstruction of crystallinity was achieved after annealing the radiation
damage at 800 deg. C, which resulted in full restoration of the RS spectrum.
HR-TEM images show, however, that the spatial distributions of NC-Ge changed as
a result of irradiation and annealing. A sharp decrease in NC distribution
towards the SiO2 surface has been observed. This was accompanied by XPS
detection of Ge oxides and elemental Ge within both the surface and subsurface
region
Euclidean-signature Supergravities, Dualities and Instantons
We study the Euclidean-signature supergravities that arise by compactifying
D=11 supergravity or type IIB supergravity on a torus that includes the time
direction. We show that the usual T-duality relation between type IIA and type
IIB supergravities compactified on a spatial circle no longer holds if the
reduction is performed on the time direction. Thus there are two inequivalent
Euclidean-signature nine-dimensional maximal supergravities. They become
equivalent upon further spatial compactification to D=8. We also show that
duality symmetries of Euclidean-signature supergravities allow the harmonic
functions of any single-charge or multi-charge instanton to be rescaled and
shifted by constant factors. Combined with the usual diagonal dimensional
reduction and oxidation procedures, this allows us to use the duality
symmetries to map any single-charge or multi-charge p-brane soliton, or any
intersection, into its near-horizon regime. Similar transformations can also be
made on non-extremal p-branes. We also study the structures of duality
multiplets of instanton and (D-3)-brane solutions.Comment: Latex, 50 pages, typos corrected and references adde
Random access quantum information processors
Qubit connectivity is an important property of a quantum processor, with an
ideal processor having random access -- the ability of arbitrary qubit pairs to
interact directly. Here, we implement a random access superconducting quantum
information processor, demonstrating universal operations on a nine-bit quantum
memory, with a single transmon serving as the central processor. The quantum
memory uses the eigenmodes of a linear array of coupled superconducting
resonators. The memory bits are superpositions of vacuum and single-photon
states, controlled by a single superconducting transmon coupled to the edge of
the array. We selectively stimulate single-photon vacuum Rabi oscillations
between the transmon and individual eigenmodes through parametric flux
modulation of the transmon frequency, producing sidebands resonant with the
modes. Utilizing these oscillations for state transfer, we perform a universal
set of single- and two-qubit gates between arbitrary pairs of modes, using only
the charge and flux bias of the transmon. Further, we prepare multimode
entangled Bell and GHZ states of arbitrary modes. The fast and flexible
control, achieved with efficient use of cryogenic resources and control
electronics, in a scalable architecture compatible with state-of-the-art
quantum memories is promising for quantum computation and simulation.Comment: 7 pages, 5 figures, supplementary information ancillary file, 21
page
On the discrete spectrum of quantum layers
Consider a quantum particle trapped between a curved layer of constant width
built over a complete, non-compact, smooth surface embedded in
. We assume that the surface is asymptotically flat in the sense
that the second fundamental form vanishes at infinity, and that the surface is
not totally geodesic. This geometric setting is known as a quantum layer. We
consider the quantum particle to be governed by the Dirichlet Laplacian as
Hamiltonian. Our work concerns the existence of bound states with energy
beneath the essential spectrum, which implies the existence of discrete
spectrum. We first prove that if the Gauss curvature is integrable, and the
surface is weakly -parabolic, then the discrete spectrum is non-empty.
This result implies that if the total Gauss curvature is non-positive, then the
discrete spectrum is non-empty. We next prove that if the Gauss curvature is
non-negative, then the discrete spectrum is non-empty. Finally, we prove that
if the surface is parabolic, then the discrete spectrum is non-empty if the
layer is sufficiently thin.Comment: Clarifications and corrections to previous version, conjecture from
previous version is proven here (Theorem 1.5), additional references include
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